A good, simple first test is Memtest86+. Grab it, burn it, boot to it, and make sure the system can run one full pass on the memory with no errors. Then, boot to windows... I'd get Prime95 to start. It should absolutely be able to run the torture test on "blend" for at least 24 hours with no crashes, warnings, or errors.
Assuming you pass those two basic tests, I'd test the GPU. There are some special-purpose GPU testers out there, but I'm not really a big fan. Many of them seemed designed to crash the system, even if you'd otherwise never see any real problems. If you don't have any newer high-end games to test with, I'd try running a few passes of FutureMark's 3DMark. That should push the GPU pretty hard, but in a realistic manner. Make sure you download and install the LATEST drivers for your graphics card before starting, even if 3DMark warns that they aren't "certified" (you don't care about publishing your score and showing off, just testing).
Memtest86+:
http://www.memtest.org/Prime95:
http://www.mersenne.org/freesoft/3DMark Vantage:
http://www.futuremark.com/benchmarks/3dmarkvantage/download/