First thing I'd do;
Get the ultimate boot cd, boot from it and run a 30 minute memory test.
Then, run a full check on each hard drive
Do a full virus scan, maybe take the drive out and put it in a PC you know has updated virus scanner.
Then what I'd do is;
Upgrade the graphics card drivers to the latest versions
Check on if there is any funny programs running in the background and disable them.
Try using a different PSU.
See what happens after this, I'd get more complicated, but in this case, I bet I'd have fixed the problem.