Hi John !
There are several things that you may try to fix your problem. At 1st, try to plug it somewhere else. Then, try resetting your SMC. To do that :
* Unplug your Mac
* Press the power for (at least) 5 seconds while unplugged
* Plug it in again then wait approx 10s before trying to start it.
You may know that power supplies on Macs are pretty strong. I'd say that your MotherBoard is dead if the previous reset does not work. You may test each of these components before replacing one (of mabe them both).
Hoping to have helped you,
Don't forget to give us some feedback !
Vincent