I installed Linux Mint, and in the process removed Windows 7 (the C:\ drive was corrupted). I had a backup, fortunately, so I reformatted the drive and restored the backup. Linux Mint recognizes the drive and all its files, GParted says it's a-ok, and GRUB recognizes it as an operating system. But when I try to boot to Windows 7, it spits out "Invalid EFI file path". Now, this seemed similar to this thread's situation, so I ran bootinfoscript (post 4), which gave this:
Code:
                  Boot Info Script 0.61      [1 April 2012]



============================= Boot Info Summary: ===============================


 => No boot loader is installed in the MBR of /dev/sda.
 => Grub2 (v1.97-1.98) is installed in the MBR of /dev/sdb and looks at sector 
    1 of the same hard drive for core.img. core.img is at this location and 
    looks in partition 2 for /boot/burg.


sda1: __________________________________________________________________________


    File system:       vfat
    Boot sector type:  -
    Boot sector info:  No errors found in the Boot Parameter Block.
    Operating System:  
    Boot files:        /efi/linuxmint/grubx64.efi


sda2: __________________________________________________________________________


    File system:       ext4
    Boot sector type:  -
    Boot sector info: 
    Operating System:  Linux Mint 14 Nadia
    Boot files:        /boot/grub/grub.cfg /boot/burg/burg.cfg /etc/fstab 
                       /boot/extlinux/extlinux.conf /boot/burg/core.img


sda3: __________________________________________________________________________


    File system:       swap
    Boot sector type:  -
    Boot sector info: 


sdb1: __________________________________________________________________________


    File system:       ntfs
    Boot sector type:  Windows Vista/7: NTFS
    Boot sector info:  No errors found in the Boot Parameter Block.
    Operating System:  Windows 7
    Boot files:        /bootmgr /Boot/BCD /Windows/System32/winload.exe 
                       /wubildr /wubildr.mbr


sdb3: __________________________________________________________________________


    File system:       ntfs
    Boot sector type:  Windows Vista/7: NTFS
    Boot sector info:  According to the info in the boot sector, sdb3 has 
                       40550399 sectors, but according to the info from 
                       fdisk, it has 40963823 sectors.
    Operating System:  
    Boot files:        /bootmgr /boot/bcd


============================ Drive/Partition Info: =============================


Drive: sda _____________________________________________________________________


Disk /dev/sda: 64.0 GB, 64023257088 bytes
255 heads, 63 sectors/track, 7783 cylinders, total 125045424 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes


Partition  Boot  Start Sector    End Sector  # of Sectors  Id System


/dev/sda1                   1   125,045,423   125,045,423  ee GPT




GUID Partition Table detected.


Partition    Start Sector    End Sector  # of Sectors System
/dev/sda1              34       195,346       195,313 EFI System partition
/dev/sda2         195,347   108,474,643   108,279,297 Data partition (Windows/Linux)
/dev/sda3     108,474,644   125,045,374    16,570,731 Swap partition (Linux)


Drive: sdb _____________________________________________________________________


Disk /dev/sdb: 750.2 GB, 750156374016 bytes
255 heads, 63 sectors/track, 91201 cylinders, total 1465149168 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 4096 bytes


Partition  Boot  Start Sector    End Sector  # of Sectors  Id System


/dev/sdb1    *          1,979 1,424,185,343 1,424,183,365   7 NTFS / exFAT / HPFS
/dev/sdb3       1,424,185,344 1,465,149,167    40,963,824  12 Compaq diagnostics




"blkid" output: ________________________________________________________________


Device           UUID                                   TYPE       LABEL


/dev/sda1        1C97-E85B                              vfat       
/dev/sda2        aadfc00d-845a-4085-a610-a77d4c8a0303   ext4       
/dev/sda3        a534fe8a-1366-47e1-bb4a-84ac33edc986   swap       
/dev/sdb1        49EF34B75D4CF4DA                       ntfs       
/dev/sdb3        8AFADDE7FADDCF95                       ntfs       LENOVO_PART


================================ Mount points: =================================


Device           Mount_Point              Type       Options


/dev/sda1        /boot/efi                vfat       (rw)
/dev/sda2        /                        ext4       (rw,errors=remount-ro)
/dev/sdb1        /media/sdb1              fuseblk    (rw,nosuid,nodev,allow_other,blksize=4096)
/dev/sdb3        /media/LENOVO_PART       fuseblk    (rw,nosuid,nodev,allow_other,default_permissions,blksize=4096)




=========================== sda2/boot/grub/grub.cfg: ===========================


--------------------------------------------------------------------------------
#
# DO NOT EDIT THIS FILE
#
# It is automatically generated by grub-mkconfig using templates
# from /etc/grub.d and settings from /etc/default/grub
#


### BEGIN /etc/grub.d/00_header ###
if [ -s $prefix/grubenv ]; then
  set have_grubenv=true
  load_env
fi
set default="0"


if [ x"${feature_menuentry_id}" = xy ]; then
  menuentry_id_option="--id"
else
  menuentry_id_option=""
fi


export menuentry_id_option


if [ "${prev_saved_entry}" ]; then
  set saved_entry="${prev_saved_entry}"
  save_env saved_entry
  set prev_saved_entry=
  save_env prev_saved_entry
  set boot_once=true
fi


function savedefault {
  if [ -z "${boot_once}" ]; then
    saved_entry="${chosen}"
    save_env saved_entry
  fi
}


function recordfail {
  set recordfail=1
  if [ -n "${have_grubenv}" ]; then if [ -z "${boot_once}" ]; then save_env recordfail; fi; fi
}


function load_video {
  if [ x$feature_all_video_module = xy ]; then
    insmod all_video
  else
    insmod efi_gop
    insmod efi_uga
    insmod ieee1275_fb
    insmod vbe
    insmod vga
    insmod video_bochs
    insmod video_cirrus
  fi
}


if [ x$feature_default_font_path = xy ] ; then
   font=unicode
else
insmod part_gpt
insmod ext2
set root='hd0,gpt2'
if [ x$feature_platform_search_hint = xy ]; then
  search --no-floppy --fs-uuid --set=root --hint-bios=hd0,gpt2 --hint-efi=hd0,gpt2 --hint-baremetal=ahci0,gpt2  aadfc00d-845a-4085-a610-a77d4c8a0303
else
  search --no-floppy --fs-uuid --set=root aadfc00d-845a-4085-a610-a77d4c8a0303
fi
    font="/usr/share/grub/unicode.pf2"
fi


if loadfont $font ; then
  set gfxmode=auto
  load_video
  insmod gfxterm
  set locale_dir=$prefix/locale
  set lang=en_US
  insmod gettext
fi
terminal_output gfxterm
if [ "${recordfail}" = 1 ]; then
  set timeout=-1
else
  set timeout=5
fi
### END /etc/grub.d/00_header ###


### BEGIN /etc/grub.d/05_debian_theme ###
set menu_color_normal=white/black
set menu_color_highlight=black/light-gray
### END /etc/grub.d/05_debian_theme ###


### BEGIN /etc/grub.d/06_mint_theme ###
set menu_color_normal=white/black
set menu_color_highlight=white/light-gray
### END /etc/grub.d/06_mint_theme ###


### BEGIN /etc/grub.d/10_linux ###
function gfxmode {
    set gfxpayload="$1"
    if [ "$1" = "keep" ]; then
        set vt_handoff=vt.handoff=7
    else
        set vt_handoff=
    fi
}
if [ ${recordfail} != 1 ]; then
  if [ -e ${prefix}/gfxblacklist.txt ]; then
    if hwmatch ${prefix}/gfxblacklist.txt 3; then
      if [ ${match} = 0 ]; then
        set linux_gfx_mode=keep
      else
        set linux_gfx_mode=text
      fi
    else
      set linux_gfx_mode=text
    fi
  else
    set linux_gfx_mode=keep
  fi
else
  set linux_gfx_mode=text
fi
export linux_gfx_mode
if [ "$linux_gfx_mode" != "text" ]; then load_video; fi
menuentry 'Linux Mint 14 Cinnamon 64-bit, 3.5.0-17-generic (/dev/sda2)' --class gnu-linux --class gnu --class os {
    recordfail
    gfxmode $linux_gfx_mode
    insmod gzio
    insmod part_gpt
    insmod ext2
    set root='hd0,gpt2'
    if [ x$feature_platform_search_hint = xy ]; then
      search --no-floppy --fs-uuid --set=root --hint-bios=hd0,gpt2 --hint-efi=hd0,gpt2 --hint-baremetal=ahci0,gpt2  aadfc00d-845a-4085-a610-a77d4c8a0303
    else
      search --no-floppy --fs-uuid --set=root aadfc00d-845a-4085-a610-a77d4c8a0303
    fi
    linux    /boot/vmlinuz-3.5.0-17-generic root=UUID=aadfc00d-845a-4085-a610-a77d4c8a0303 ro   
    initrd    /boot/initrd.img-3.5.0-17-generic
}
menuentry 'Linux Mint 14 Cinnamon 64-bit, 3.5.0-17-generic (/dev/sda2) -- recovery mode' --class gnu-linux --class gnu --class os {
    recordfail
    insmod gzio
    insmod part_gpt
    insmod ext2
    set root='hd0,gpt2'
    if [ x$feature_platform_search_hint = xy ]; then
      search --no-floppy --fs-uuid --set=root --hint-bios=hd0,gpt2 --hint-efi=hd0,gpt2 --hint-baremetal=ahci0,gpt2  aadfc00d-845a-4085-a610-a77d4c8a0303
    else
      search --no-floppy --fs-uuid --set=root aadfc00d-845a-4085-a610-a77d4c8a0303
    fi
    echo    'Loading Linux 3.5.0-17-generic ...'
    linux    /boot/vmlinuz-3.5.0-17-generic root=UUID=aadfc00d-845a-4085-a610-a77d4c8a0303 ro recovery nomodeset 
    echo    'Loading initial ramdisk ...'
    initrd    /boot/initrd.img-3.5.0-17-generic
}
### END /etc/grub.d/10_linux ###


### BEGIN /etc/grub.d/10_lupin ###
### END /etc/grub.d/10_lupin ###


### BEGIN /etc/grub.d/20_linux_xen ###


### END /etc/grub.d/20_linux_xen ###


### BEGIN /etc/grub.d/20_memtest86+ ###
### END /etc/grub.d/20_memtest86+ ###


### BEGIN /etc/grub.d/30_os-prober ###
menuentry 'Windows 7 (loader) (on /dev/sdb1)' --class windows --class os $menuentry_id_option 'osprober-chain-49EF34B75D4CF4DA' {
    insmod part_msdos
    insmod ntfs
    set root='hd1,msdos1'
    if [ x$feature_platform_search_hint = xy ]; then
      search --no-floppy --fs-uuid --set=root --hint-bios=hd1,msdos1 --hint-efi=hd1,msdos1 --hint-baremetal=ahci1,msdos1  49EF34B75D4CF4DA
    else
      search --no-floppy --fs-uuid --set=root 49EF34B75D4CF4DA
    fi
    chainloader +1
}
menuentry 'Windows Recovery Environment (loader) (on /dev/sdb3)' --class windows --class os $menuentry_id_option 'osprober-chain-8AFADDE7FADDCF95' {
    insmod part_msdos
    insmod ntfs
    set root='hd1,msdos3'
    if [ x$feature_platform_search_hint = xy ]; then
      search --no-floppy --fs-uuid --set=root --hint-bios=hd1,msdos3 --hint-efi=hd1,msdos3 --hint-baremetal=ahci1,msdos3  8AFADDE7FADDCF95
    else
      search --no-floppy --fs-uuid --set=root 8AFADDE7FADDCF95
    fi
    drivemap -s (hd0) ${root}
    chainloader +1
}
### END /etc/grub.d/30_os-prober ###


### BEGIN /etc/grub.d/30_uefi-firmware ###
### END /etc/grub.d/30_uefi-firmware ###


### BEGIN /etc/grub.d/40_custom ###
# This file provides an easy way to add custom menu entries.  Simply type the
# menu entries you want to add after this comment.  Be careful not to change
# the 'exec tail' line above.
### END /etc/grub.d/40_custom ###


### BEGIN /etc/grub.d/41_custom ###
if [ -f  ${config_directory}/custom.cfg ]; then
  source ${config_directory}/custom.cfg
elif [ -z "${config_directory}" -a -f  $prefix/custom.cfg ]; then
  source $prefix/custom.cfg;
fi
### END /etc/grub.d/41_custom ###
--------------------------------------------------------------------------------


=========================== sda2/boot/burg/burg.cfg: ===========================


--------------------------------------------------------------------------------
#
# DO NOT EDIT THIS FILE
#
# It is automatically generated by /usr/sbin/burg-mkconfig using templates
# from /etc/burg.d and settings from /etc/default/burg
#


### BEGIN /etc/burg.d/00_header ###
set theme_name=burg
set gfxmode=640x480
if [ -s $prefix/burgenv ]; then
  load_env
fi
set default="0"
if [ ${prev_saved_entry} ]; then
  set saved_entry=${prev_saved_entry}
  save_env saved_entry
  set prev_saved_entry=
  save_env prev_saved_entry
  set boot_once=true
fi


function savedefault {
  if [ -z ${boot_once} ]; then
    saved_entry=${chosen}
    save_env saved_entry
  fi
}
function select_menu {
  if menu_popup -t template_popup theme_menu ; then
    free_config template_popup template_subitem menu class screen
    load_config ${prefix}/themes/${theme_name}/theme ${prefix}/themes/custom/theme_${theme_name}
    save_env theme_name
    menu_refresh
  fi
}
function toggle_fold {
  if test -z $theme_fold ; then
    set theme_fold=1
  else
    set theme_fold=
  fi
  save_env theme_fold
  menu_refresh
}
function select_resolution {
  if menu_popup -t template_popup resolution_menu ; then
    menu_reload_mode
    save_env gfxmode
  fi
}
if test -f ${prefix}/themes/${theme_name}/theme ; then
  insmod coreui
  menu_region.text
  load_string '+theme_menu { -arabic_and_freedom { command="set theme_name=arabic_and_freedom" }}'
  load_string '+theme_menu { -black_and_white { command="set theme_name=black_and_white" }}'
  load_string '+theme_menu { -burg { command="set theme_name=burg" }}'
  load_string '+theme_menu { -chiva { command="set theme_name=chiva" }}'
  load_string '+theme_menu { -coffee { command="set theme_name=coffee" }}'
  load_string '+theme_menu { -minimum { command="set theme_name=minimum" }}'
  load_string '+theme_menu { -proto { command="set theme_name=proto" }}'
  load_string '+theme_menu { -radiance { command="set theme_name=radiance" }}'
  load_string '+theme_menu { -radiancetext { command="set theme_name=radiancetext" }}'
  load_string '+theme_menu { -refit { command="set theme_name=refit" }}'
  load_string '+theme_menu { -sora { command="set theme_name=sora" }}'
  load_string '+theme_menu { -sora_clean { command="set theme_name=sora_clean" }}'
  load_string '+theme_menu { -sora_extended { command="set theme_name=sora_extended" }}'
  load_string '+theme_menu { -ubuntu { command="set theme_name=ubuntu" }}'
  load_string '+theme_menu { -ubuntu2 { command="set theme_name=ubuntu2" }}'
  load_string '+theme_menu { -winter { command="set theme_name=winter" }}'
  load_config ${prefix}/themes/conf.d/10_hotkey
  load_config ${prefix}/themes/${theme_name}/theme ${prefix}/themes/custom/theme_${theme_name}
  insmod vbe
  insmod png
  insmod jpeg
  set gfxfont="Unifont Regular 16"
  menu_region.gfx
  vmenu resolution_menu
  controller.ext
fi
insmod ext2
set root='(hd0,2)'
search --no-floppy --fs-uuid --set aadfc00d-845a-4085-a610-a77d4c8a0303
set locale_dir=($root)/boot/burg/locale
set lang=en
insmod gettext
set timeout=5
### END /etc/burg.d/00_header ###


### BEGIN /etc/burg.d/10_linux ###
menuentry 'LinuxMint GNU/Linux, with Linux 3.5.0-17-generic' --class linuxmint --class gnu-linux --class gnu --class os --group group_main {
    insmod ext2
    set root='(hd0,2)'
    search --no-floppy --fs-uuid --set aadfc00d-845a-4085-a610-a77d4c8a0303
    echo    'Loading Linux 3.5.0-17-generic ...'
    linux    /boot/vmlinuz-3.5.0-17-generic root=UUID=aadfc00d-845a-4085-a610-a77d4c8a0303 ro  quiet splash
    echo    'Loading initial ramdisk ...'
    initrd    /boot/initrd.img-3.5.0-17-generic
}
menuentry 'LinuxMint GNU/Linux, with Linux 3.5.0-17-generic (recovery mode)' --class linuxmint --class gnu-linux --class gnu --class os --group group_main {
    insmod ext2
    set root='(hd0,2)'
    search --no-floppy --fs-uuid --set aadfc00d-845a-4085-a610-a77d4c8a0303
    echo    'Loading Linux 3.5.0-17-generic ...'
    linux    /boot/vmlinuz-3.5.0-17-generic root=UUID=aadfc00d-845a-4085-a610-a77d4c8a0303 ro single 
    echo    'Loading initial ramdisk ...'
    initrd    /boot/initrd.img-3.5.0-17-generic
}
### END /etc/burg.d/10_linux ###


### BEGIN /etc/burg.d/30_os-prober ###
menuentry "Windows 7 (loader) (on /dev/sdb1)" --class windows --class os {
    insmod ntfs
    set root='(hd1,1)'
    search --no-floppy --fs-uuid --set 49ef34b75d4cf4da
    chainloader +1
}
menuentry "Windows Recovery Environment (loader) (on /dev/sdb3)" --class windows --class os {
    insmod ntfs
    set root='(hd1,3)'
    search --no-floppy --fs-uuid --set 8afadde7faddcf95
    drivemap -s (hd0) ${root}
    chainloader +1
}
### END /etc/burg.d/30_os-prober ###


### BEGIN /etc/burg.d/40_custom ###
# This file provides an easy way to add custom menu entries.  Simply type the
# menu entries you want to add after this comment.  Be careful not to change
# the 'exec tail' line above.
### END /etc/burg.d/40_custom ###
--------------------------------------------------------------------------------


=============================== sda2/etc/fstab: ================================


--------------------------------------------------------------------------------
# /etc/fstab: static file system information.
#
# <file system> <mount point>   <type>  <options>       <dump>  <pass>


proc    /proc    proc    nodev,noexec,nosuid    0    0
#Entry for /dev/sda2 :
UUID=aadfc00d-845a-4085-a610-a77d4c8a0303    /    ext4    errors=remount-ro    0    1
#Entry for /dev/sda1 :
UUID=1C97-E85B    /boot/efi    vfat    defaults    0    1
#Entry for /dev/sdb3 :
UUID=8AFADDE7FADDCF95    /media/LENOVO_PART    ntfs    defaults,nls=utf8,umask=0222    0    0
#Entry for /dev/sdb1 :
UUID=49EF34B75D4CF4DA    /media/sdb1    ntfs-3g    defaults,locale=en_US.UTF-8    0    0
#Entry for /dev/sda3 :
UUID=a534fe8a-1366-47e1-bb4a-84ac33edc986    none    swap    sw    0    0




--------------------------------------------------------------------------------


====================== sda2/boot/extlinux/extlinux.conf: =======================


--------------------------------------------------------------------------------
## /boot/extlinux/extlinux.conf
##
## IMPORTANT WARNING
##
## The configuration of this file is generated automatically.
## Do not edit this file manually, use: extlinux-update




default l0
prompt 1
timeout 50


include themes/debian/theme.cfg
--------------------------------------------------------------------------------


=================== sda2: Location of files loaded by Grub: ====================


           GiB - GB             File                                 Fragment(s)


  44.359673977 = 47.630837248   boot/burg/burg.cfg                             2
   4.222077847 = 4.533421568    boot/burg/core.img                             1
  44.447198391 = 47.724815872   boot/grub/grub.cfg                             1
  44.302648067 = 47.569606144   boot/initrd.img-3.5.0-17-generic               1
   4.226899624 = 4.538598912    boot/vmlinuz-3.5.0-17-generic                  1
  44.302648067 = 47.569606144   initrd.img                                     1
  44.302648067 = 47.569606144   initrd.img.old                                 1
   4.226899624 = 4.538598912    vmlinuz                                        1


================= sda2: Location of files loaded by Syslinux: ==================


           GiB - GB             File                                 Fragment(s)


   4.221810818 = 4.533134848    boot/extlinux/chain.c32                        1
   4.273004055 = 4.588103168    boot/extlinux/extlinux.conf                    1


============== sda2: Version of COM32(R) files used by Syslinux: ===============


 boot/extlinux/chain.c32            :  COM32R module (v4.xx)
I lost the thread (no pun intended) from there. Any ideas?