[Faceman]

probably bad memory although normally this would lead to not starting and giving you an according speaker beep sequence (codes can be found on your Mainboard manufacturer's page most likely)
There are basically four components that can be responsible for "PC not starting" (wrongly connected cables and stuff aside; just talking about hardware faults)

would be great help if you could tell us your configuration (which CPU, MB, RAM, VGA,...)

CPU - check for physical damage and try substitution if you have a spare
Mainboard - try monitoring the LEDs and beeps upon start up (open case of course)
RAM - if you have more than one stick try every one as a single. borrow a RAM stick from a friend to see of the problem lies here
VGA adapter - PC should still start but with no/faulty screen, try disconnecting VGA adapter -> you should get a warning beep sequence but machine should boot up fine.

keep in mind that a damaged CPU or Mainboard can result in a false voltage thus damaging/destroying up to all the other components (although mostly the CPU, RAM and Mainboard are affected)