whats your power supply rating and manufacturer? Also good be your memory, software memory testers may not catch all errors, but they catch most. Here's a decent (very decent for free) one:
http://www.majorgeeks.com/download.php?det=3955
and if you want to check the CPU on your machine, try this: http://www.majorgeeks.com/download.php?det=273

Reason why I ask about your power supply is that a under rated power supply can cause lock-ups too. Just some back ground on the machine:
Is this a recent problem on the machine?
If yes has anything been added (software or hardware) to the machine?
If no, how long has this been occuring, and can you think of anything, anything at all, that might be related to this behavior?
If you think it's your video card, really simple way to fine out is go by a tech shop, ask one of the tech guys if they have an old, piece of crap PCI graphics card they want to sell (don't pay more than $10 for an old Trident 4MB PCI). Uninstall your graphics card (drivers and all in device manager), install the crap one, and see if you experience the same problems.
You can try moving to a different power outlet. Sounds silly, but can cause problems. Also, you can get what they call a line conditioner for your power (basically a really nice power strip. Same think UPS's use without the battery part. Cost about $25. If you buy it from Wal-Mart, and it doesnt work, you can take it back and get your money back, tax included) It basically smooths the power out to your machine if the outlet you are using is causing sporadic power spikes/dips. Etc... let me know