ss1133xx; welp, like this
indicates to me that you are not booting from a liveDVD/USB
mkdir: cannot create directory `/mnt/work': File exists
indicates to me that you did not use the appropriate username for whatever the username you use for the system that is installed to sda1.
mint@mint ~ $ ls -la /mnt/work/home/<mint@mint>
We need to mount sda1 OR sda6, depending on what you have for the liveDVD/USB - to match -.
Once the match is established, we can try and install grub once more ( looking like we should be working from sda6, instead of sda1, huh ?)
There is absolutely no reason that I know of - short of a corrupted file system - that prevents mounting and accessing to see what is on those partitions, to determine absolutely what operating system we are working with.
so once more try:
Boot the liveDVD/USB to a terminal;
sudo mkdir /mnt/work ##from the liveDVD this mount point will not persist
sudo mount /dev/sda1 /mnt/work
##Now the install on sda1 is accessable, let's look:
ls -la /mnt/work/home/the_user_name_for_the_system_on_sda1
##because we are mounting sda1##
##while we are here:##
ls -la /mnt/work/boot
##for a listing of the kernels, so I know weather to use "root" or "boot" as the grub install target.##
"ls -la /mnt/work/home/sysop" where "sysop" is my user_name
I believe once we have the partitions matched to the liveDVD/USB, we can (RE-)install grub.
ain't nothing but a thing