This is the corruption.
/dev/sda1 overlaps with /dev/sda2
Note that sda6's end is one sector less than sda2's, and that should be then end of the sda1 also.
The end of sda1 cannot be after the start of sda2.
/dev/sda1 2,047 664,801,829 664,799,783 f W95 Extended (LBA)
/dev/sda5 2,048 660,602,879 660,600,832 83 Linux
/dev/sda6 660,604,928 664,797,183 4,192,256 82 Linux swap / Solaris
/dev/sda2 664,797,184 665,001,983 204,800 7 NTFS / exFAT / HPFS
First backup partition table, use your drive for sdX or sda, sdb etc.
sudo sfdisk -d /dev/sdX > parts.txt
Many partition tools calculate the extended partition entry and just re-saving may correct it.
this occasionally fixes issues and is worth trying:
you do the following :
use option : x (expert mode)
use option : p (to print)
use option : v to verify partition
if it is ok
then you can do
option : w ( to write table to disk)
option : q to quit
Fixparts is not for overlapping partitions, but again it recalculates table and since in your case it is the extended it may work also.
Fixparts - Repair broken partition tables (not overlapping issues) & delete Stray gpt data from MBR drives
Windows normally creates the hidden in Windows 100MB boot partition. It also has Windows recovery (repair or f8). But many users just delete it as they do not know it is essential. So Boot-Repair copies boot files to main install and then grub2's os-prober finds both. You can boot either and f8 may not work if booting the 100MB form grub as it is very quick. Best just to use Windows to make its own repair flash drive.
Make your own Windows repairCD (not vendor recovery):
Windows users only - Silverlight
Windows 7 repair USB, Also Vista if service pack installed