Hi!
[1] Test to see if your power brick (external AC adapter) is working.
If you have a green light on the back of the unit when everything is plugged in, my first assumption is that the brick is working.
[2] if you get a brief sound of fan noise, and a brief blue light in the front, this is a sign that the internal sensors for power are shutting down the machine as soon as it detects a short or some other problem in the internal PSU or mother board.
[3] If you have recently moved the unit (before the problem) I would re seat the memory and hard drive connections. (This is really a forlorn hope kind of fix. It is hoping that an easy to fix problem is the one you have, but it is almost certainly not the case.)
[4] Most likely a bad capacitor in the power supply circuits or a short circuit.
I am taking the memory and hard drive out of mine as we speak since the unit is not worth saving.