We need to know what's in the computer to say for sure. Post all your components with the model numbers. Links would be great as well.
Before we start guessing at problems, you should run through the steps in the "READ before posting about boot problems" sticky (link in my signature). Make sure to do EVERY step. DO NOT SKIP any of them, as they all are checking a differenct problem. After doing ALL of the steps, come back with anything that changed.
Some other things to check. Are you getting any beep codes from the board? What lights are coming on the board?
In cases like this, a bad PSU is likely. However, the fact you said the onboard graphics isn't working leads me to believe that the motherboard might have a problem. To guess any further would be a shot in the dark without more info.