There is another way to save your files in your home directory IFF they are indeed still there:
1: Download the
EasyOS img. file using the Mint Live CD.
2: Use Mint's native USB Image Writer to burn the img. file to an USB drive.
3: Start your computer from that USB drive (you may have to tweak the BIOS in order to do so).
4: When EasyOS is up and running select the drive on the computer, navigate to the internal drive and find your home directory.
IFF there are still files there you will be able to copy them to any other location as well as the USB drive that is running EasyOS. (Provided there is enough space.)
In the end you might have to reinstall your system since it's broken but at least you will have your files back. Provided they are still there of course.