When you said the computer would come on but no power to monitor or keyboard, I am guessing you mean the keyboard lights don't flash just after turning system on.
if you have no display, no keyboard flash, no beep etc but system is powered up, then this suggests that it's not passing the POST test stage.
Check out what Nubius said about the PSU first but if it looks alright, then open up system & check eveything is seated correctly (ie cables/graphics/ram etc) and clear the bios using the jumper on the mobo.
If none of these things make any difference, then it sounds like it could be a dry joint on the montherboard. You will need to remove the mobo from the case & carefully inspect it for any loose components (eg capacitors etc) & cracks. Remember to wear a static strap, do not touch the contacts on the cards/ram/cpu & handle the mobo as little as possible.