Bret:
It may be any number of things. Try these troubleshooting steps:
1. The video card or DirectX may be the cause. Check Window's Device Manager for a conflict between your video card and some other device connected to your system. Run dxdiag (click Start > Run and type [size=16]DXDIAG[/size] and click OK. Run all the tests to make sure your Windows DirectX software is not causing the problem.
2. Check for overheating. The fact that your computer hangs when you are playing graphic-intensive games may be a sign of too much heat inside the case. Dust keeps your system from properly cooling. Buy a can of compressed air, open up the computer case, and spray out all the dust (especially the dust clogging the vents). But don't blow the dust into the case, blow it out, instead. While you have the computer case open, power up the machine and check to see that all the fans are inside the case (especially the one attached to the CPU) are spinning and not making any loud noises. If any of the fans are not working properly, take it to a computer repair shop to have them replaced.
3. The power supply (which is really a power converter) may be dying hard. If it fails to provide the proper voltages (either too much or too little voltage) the system will lock up. The fact that this happens when you start your computer means that the power supply may be the culprit. Try taking it to the shop and having them replace the power supply. If that doesn't fix it, you'll still have a spare just in case it does fail in the future (which they often do).
If those three steps don't work, let us know and one of us will make more suggestions.