I'm thinking from the lack of information provided that it might have something to do with the power supply. There might have been something fail on the motherboard itself.

It could also be the RAM, CPU, hard drive, or video Card. There''s not enough information to tell.

Before you try anything else, is power getting thru, are the fans spinning/lights on. is the HDD spinning up, you should hear it.
if all seems ok,clear the cmos.
disconnect power lead, hit the start button to drain any residual power in the system. then move the cmos jumpers across for 20 secs or so, then move them back, reconnect and see it restarts. if you dont know where the cmos jumpers are just take out the bios battery and short the contacts, it works just the same and will reset the bios.
if that doesnt work test the ram sticks by trying one at a time.

Give us some more information if you can. Sounds, lights, smells, fan blowing/spinning... etc.