If you don't know what happened that corrupted your install, I am certain that I don't know.
I can tell you how to save your data however. I am assuming you don't have a separate /home partition. If you do, don't go any further. Post back.
Use your Mint live cd, or if you have a lot of data to transfer then go to the url below and download Puppy shard 3.01 iso. It is a small, 155 MB, fast, live cd that you can use as a tool kit.
Look in the menu of the live cd desktop and open Gparted. Look and see how much spare space you have in your Mint install. The system itself should be about 4 Gig. The difference between that and the amount of space that is actually being used is mostly data. This will give you some idea of the amount of space you need to free up. Shrink your Mint install partition to just a bit more than it is occupying. Hopefully this will give you enough space to make another partition to transfer your data to. Make the new partition and format it to ext3. Close Gparted and reboot the live cd.
When the live cd comes back up, copy your /home/username folder from your Mint install to your new partition.
From here on I need a little more information.
1) How large is your disk drive?
2) How large is your Mint install?
3) Do you have a Windows install? If so, How big is it?
4) What else, if anything is on that drive?
5 Do you have more than one drive?
In fact it would be better to answer these questions first.