I assume you have no external/aftermarket graphics card so we can rule that out. What that means is you have two possible avenues to go down:
1) Motherboard is done.
2) Power supply is done.
Now, there are in my opinion, % chances for each to be the issue. I would asign the motherboard with only a 20% chance, and the power supply to be 80% most likely the issue.
The reason for this is, the computer is getting power, booting up, then failing. Most of the time if the motherboards done, it wont boot.
The solution is easy, but may be a pain in the butt. And does require some (very little) knowledge on how to put together a computer.
Just go buy a small $30 430w power supply from the local store. Hook it up and see if it runs! (most likely will be the fix)
If it's not the fix, it's the motherboard. But first let us know if the power supply is the issue after testing this.
Also, may seem silly, pop out the ram, then push them back in firm (careful).
Somtimes loose ram sticks cause silly problems.