How long before it goes off? Is it going off because it's receiving no signal? If so, it's probably a PC problem and, since your PC is a new one, you should return it under guarantee (after you've checked the obvious connections).
If it's going off while there's something displayed on the screen, it could be the display or it could be the PC. Have you got another display you can check out the PC with?
i had exactly the same problem. it was the graphics card, which in my case had faulty ram modules, and it stopped the computer from booting up at all in the end. i tested an older card in it and the system booted first time.
so new card put in and all has worked perfectly since!
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