Use a volt meter to measure the voltage on your 12-V rail (from a molex connector) while running Prime95 or memtest. If there is an obvious problem with the power supply, you will see a voltage drop on the rail.
Mind you, if you do not see a significant drop with a volt meter, that does not mean that the power supply has no problem!
The volt meter shows the average voltage. If there is bad voltage regulation, you may have too much ripple on the rail, which would cause problems. But, you would not see it on a volt meter.