To test the Power Supply, first disconnect all the cables from all the peripherals (hdd, cd-rom, fdd, mb, a.s.o.), then use a wire to connect the green wire on the connector for the MB to a black wire on the same connector. Plug the power supply to main ac, and see if the fan spins. If it spins, then use a multimeter to check the voltages on the other wires. If the voltages are ok, you should start worrying about other things.
Start the mb with nothing else but cpu and heatsink, no mem, no video or other cards.
You should hear long repeating beeps in the speaker., meaning there is no memory installed. If you don't hear them , reset the BIOS and try again. If you still don't hear them it should be the MB that is broken.
If you hear the sound, then put in the memory, but no video,
Turn on the computer, now you should hear a long beep, followed by three short ones. That means there is no video adapter installed.
Then put in the video card. If it beeps, it should be a problem with the video. then check the others.
I've had no-starts because of a fryed video adapter or a fryed network card.