Like others, I have never heard of a fully comprehensive power suply check that can be run - unless the computer is fully booted up and working. IMHO the only way to be certain is to check the voltage output at each pin of each plug when the power supply is connected to its motherboard. My post above was based on the following experience:
6 years ago, I acquired my first XP machine - a Maxdata with a service contract. After 18 months, no beeps and no startup. Summoned engineer who fitted new power supply. Normal service resumed. Two years later, no beeps and no startup - well, if you tried to switch it of and then on several times, eventually you might get a beep and startup would commence. Then it was necessary to remember NOT to switch the machine off!
Cure - fit another power supply.
Six months ago - no beep, no startup, acquired a further supply from P.C. World and problem cured - mental note to replace computer.
The other month while new dual core machine was being assembled, - No beeps, No startup. P.C. World replaced the power supply on warranty. Once again, Normal service resumed, however, new M/C now uses a power supply from a different source.
P.P.