Take a close look at the power switches and reset buttons.
Inspect any involved wires and replace any cables with a connector that seems "flimsy".
Double check that the motherboard or some component therein is not coming in contact with the case or otherwise being grounded out.
The next steps would be to begin pulling and replacing components one at a time to determine if one is faulty.
Overall it is a good sign that your build did work. May be that something just slipped or came loose once it was powered up and things heated up and/or moved.
What PSU did you use? That, in my mind, is the most likely suspect.