XPS 8950, wont power up

My XPS8950 was  working fine yesterday and shut off last night

I attempted to start it this morning

The green light at the rear of the computer, I believe it is on the power supply, came on for a couple of seconds, the power button on the front of the computer and the logo light on the video driver card all came on for the same two seconds and then there was a click, near the power switch on the front of the computer, and they all went out.

Two seconds later, without me doing anything, the  steps above were repeated and then the computer was dead.
Can someone tell me how to determine what is  wrong?  I suspect that the power supply went bad but have no idea.

Any thoughts would be appreciated.
Thank  You.