Alright, I think I've narrowed it down to the motherboard. I found a Help section in my motherboard manual that says that the system will automatically power off the system to protect the CPU from overheating. After reseating the CPU and heatsink, the computer stayed on for about 20 seconds, then shut down again. Reseating it again was met with mixed results.
I've gone through all the steps listed in the manual to fix the problem (reset CMOS, check that thermal paste is even across the surface) but nothing seems to really work. I'm about ready to return the motherboard (again). Any suggestions before I do that?
@Daniel3679: Yes, I even tried pulling out the video card, hard drive and CD-ROM drive. Still the same instant shutdown.
Edited by DuFF, 11 July 2006 - 05:33 PM.