when the system won't startup, any error message? or just black screen?
if it is a black screen, then unplug hd and cd-rom drive, only keep memory and video card, see if you can get post. if no post, then take memory or video card out, see if you have any beep sound.
if you get post, then goto bios, check the hardware monitor, check the power 3v,5v,12v if it is a right number, then you will know the power supply is good or not.
hopefully can give you some idea.....good luck.