Sure fire way to test your power supply is to short out two of the pins on the main power connector to the mainboard. These pins are always in the place - you should have a green and black wire next to each other - one will be pin 14.
Remove the connector, get a small piece of wire and short the two pins. If the power suppy comes on it is probably working fine. Do it first with nothing else connected up, then add the drives afterwards.
When going down to bare config you can also go as far as removing the video card. Your computer should beep once when you power it on as a signal that the power on self test has passed. Removing the video card should force it to give a faliure beep code.
Also powering on with the memory removed should give a faliure beep code.
We can go down to the point where all that is connected is the power supply, mainboard and CPU.
Depending on the CPU there is another thing you can try - do you know what CPU you have?