Try removing all add on cards, cables and extras other than the processor, memory, keyboard and monitor.
Try booting again.
If it works, it was an addon. If it still doesn't work, try re-seating the memory.
If it works, it was a stick that was loose, if it still doesn't, try re-seating the processor.
If it works, your computer probably took a bashing somewhere, but if it still doesn't, and you get no beep/diagnostic information, it could be a problem with the motherboard. If your machine is of a certain age (P4 era) you may want to check for faulty/damaged capacitors.