"It sounds like your file system might be corrupt, and possibly your drive is near death. The lack of ability to fsck is a bit of a clue.
I'd look at backing up whatever data I could on the existing drive. You could live CD boot, and copy it to a USB-caddy disk, or install a second drive in the case, or replace the drive and put the old one in a caddy.
If you succeed in copying, without any disk errors, you could try re-installing the system on the same drive.
If it was me though, I'd buy a new drive, stick the old one in a USB caddy, and try to get whatever I could from it before it dies.
It is possible something else is causing your problems, so if you're keen you could run a memory diagnostic, and whatever other system test code you can from your live cd, especially if you're reluctant to do a re-install. All that will cost is time.