It sounds like there is a problem with the Power Supply Unit (PSU) or a problem with your Motherboard. Could also be the video card attached to the motherboard as I have had the same issue. The motherboard had to be replaced and so did the video card. I had the same exact issue.
The main question that would help a tech when you take it in, is this. Does it show anything or is it a blank screen? If it is blank for 10 seconds and reboots, it sounds like the motherboard and video card. If it shows a pictures, sounds like the PSU.