Motherboard or processor

My friend has a problem with her PC. I have eliminated most of the hardware, and have tried booting with only RAM and processor (celeron 400) connected to the motherboard, and no POST beeps at all result. Is there any way of testing whether the fault is with the motherboard or the processor without obtaining a good processor or motherboard – don’t want to buy the wrong one!!!

N.B.: Have tried different power supplies etc.