John upgraded to Windows 7 and after installing it, it started crashing. Leo says it could be a flakey power supply, or the video card could be overheating. It's definitely a hardware failure and since it's an older computer, it was just a matter of time before it would happen. Open up the computer and make sure the fans are running on the CPU and around the computer. He can even vacuum out the dust to clean it up.
In the chatroom - Aero may be causing the crash. Turn off Aero because it may be overworking the video card. Here's an article from Microsoft Answers on how to do it.