The Ultimate Boot CD is is ideal for this as it contains most of the more commonly needed Testing Utilities and the fact that it's free doesn't hurt one little bit either
http://www.ultimatebootcd.com/download.html
The two things to test that are really important here is the HDD and the RAM.
To test the HDD you need to run ideally the Makers testing Utility on the System and then if it fails that test remove the HDD fit to another computer and retest. If it fails the second test the HDD is faulty and needs replacing so if it's still working get your Data off it immediately and scrap it. If it's dead it's gone to [b]Silicon Heaven[/b] and to all intents and purposes your Data is lost forever unless you have a Backup or lots of money.
However if it p[asses the test in the Second Computer that Drive is Perfectly functional so either the M'Board, The Power Supply or the Data Lead in the original computer is faulty. You need to repeat the test with one component at a time from the First System to rule out or find the faulty component.
As for the RAM there are several possibilities particularly if more has been fitted since new the most likely thing is that there is a Mismatch between the different RAM Modules which particularly when installing Windows can cause problems. If that is the case here and all RAM Tests as OK individually but fails the test when it's all fitted to the M'Board you have a Timing Issue and the only real way around this is to fit Matched RAM Modules to get away from the Timing Issue. These RAM Modules would need to come from the same Maker be the same Model and ideally from the same Product Run so that differences between the different Modules will be as little as possible.
However if the RAM Passes the Tests but will not allow Windows to Install simply removing all but 1 Module finish the Windows Install and then when Windows is up and Running refit the remainder of the RAM things will be OK.
Col