I think I am spoiled because I have worked in IT for the last 5 years and with computers in general for the last 20...I always have a spare drive, drive enclosure, RAM, etc. to work with. I would say try to get your hands on another hard drive - even if it is just a 6GB or something for real cheap and try a reinstall of your OS.
Another thing to try is a Knoppix CD. Knoppix, if you are not familiar, is a complete OS and suite of applications that runs entirely off of a CD. No changes are made to your system at all. Simply download the disc from http://www.knoppix.net/get.php
, pop it in, make sure your system is configured to boot off of the CD, and in a short while you should be up and running. Knoppix should be able to mount your hard drive and allow you to browse the files, etc. It may even have support for your networking components and allow you to backup your files to a network location.
I would think that if the system works off of a Knoppix CD, then that would rule out heat as an issue, general PC components, and would more strongly point the finger at the hard drive. If it doesn't run under Knoppix, then I would say it is safe to say that the problem is NOT your hard drive, and start looking at other things.
If you have two sticks of RAM, try swapping them out, and running off of one, then the other, also switching RAM slots - to rule out RAM.
Just some more things to think about.