I would try a different power supply, just to be sure that is not the problem. If it locks after only 5 minutes, that does not sound like heat - but if it is really dirty inside the case, it could still be a heat issue.
Failing RAM can do this too. You can test RAM using one of the following programs. Both require you to create and boot to a bootable floppy disk or CD to run the diagnostics. Using the floppy method is generally easier (and another reason to include floppy drives in new builds). However, the CD method is just as effective at detecting RAM problems. Allow the diagnostics to run for several passes or even overnight. You should have
no reported errors.
Windows Memory Diagnostic - see the easy to follow instructions under Quick Start Information.
or
MemTest86+ (for more advanced users) - an excellent how-to guide is available here.
Alternatively, you could install a single RAM module and try running with that to see if it fails. Repeat process with remaining modules, hopefully identifying the bad stick through a process of elimination.
