Interesting problem here with one of my computers that probably isnt even OS related.

Fedora Core 4 running on the computer and I usually do not shut this PC off. This morning it had shut itself on. It gets to "Ok booting the kernel...." then just shuts off. I went to work and figured it was faulty RAM and I would just find the culprit and remove it when I got home.

There are two sticks of RAM in this computer, lets call them A and B.
I removed stick A...and the kernel booted. However, a few minutes later it did the same thing after logging into X...crashed. So I did a swap again and, put A back in and removed B. It crashed much quicker this time. Tried to load a Fedora install (just to make sure it wasnt my current installation) and got crashing.

I took both sticks of RAM out and decided to try them on a computer I knew that was working. They both worked fine with no crashes. Any suggestions? Could the seats for the RAM just be dirty or something? Maybe not RAM?

Thanks in advance

Could be a bad motherboard. Or a bad hard disk. Try a CD Linux to rule out the HD. Inspect the motherboad for bad capacitors.