Most likely the PSU, bad memory or bad board.

Bad memory you should be able to test by swapping them around and single sticking it, but I doubt this is it.

Bad power supply is most easily tested by bringing your case into a shop that can test it for you. You might see if they have a bench power supply they can hook it up to as well as a power supply tested since the larger power supplies are somtimes harder to troubleshoot since they occasionally fail only under heavy load. In order to do this (if they don't understand what you are asking) just hook up MB, video and primary HD and see if it still won't power on.