Immediately after posting, I set about installing openSUSE 11.4 so I would at least have a functioning machine. After running this new install for about a day, I haven't encountered a single problem.
The longer it runs clean, the more probable your solution.
In cases where you need to separate hardware from software problems, you need to replace one of them to eliminate one or the other. In this case it looks like Windows 7, though it's a bit suspicious that it ran OK initially. I assume the media you re-installed it from is OK?
Overtemping can cause hangs, check fans and cooling, as catkin mentions above, along with stripping down to what's known as a "minimal system" is a good idea if the problem persists. You'd then need to add back additional memory and adapter cards one at a time till the problem reoccurs. The last thing fitted is then suspect. Note you may have to run for quite a while before each additional part is re-installed to be confident. (Saves buying replacement parts, just takes longer)
I agree with TobiSGD regarding Condensers/Capacitors. You get the end caps on electrolytic ones deforming and/or leaking, usually to do with the DC power feed on the motherboard or the processor's voltage control circuitry. This causes spurious power problems which can cause hangs and other random problems.
Good luck and Play Bonny!