first thing to try is to remove the processor, memory and video card (if it has one) and clean their contacts and the slot they came from, put them back and see if that helps.
the processor will probably need new thermal paste - but for this test to just to get the PC to boot, you'll be fine.
has the PC been in use and this problem has suddenly happened?
during bootup, can you get into the BIOS? (usual keys are Del, Esc or F2, but since you have no display, this is probably NO)
is the PC getting power, that is, are LED's flashing, hard drives spinning and fans whirring when you start it?