Screen goes black

Hello,
I just received a custom built gaming computer. It ran fine until I hooked up to Qwest, got online and started playing World of Warcraft. Now, after about 10-15 minutes, the background will go black, but I still have a few viewable items in the foreground. Not believing that this could possibly be my video card (as I have a very powerful one), I lowered all in game graphics and still have the same problem. The background turns black, I press Ctrl Alt Delete and am able to click back into the game, play for 10 min, it happens again, except the second time when I press Ctrl Alt Delete, it won't allow me to get out of the game AND it is now happening even when I'm not playing WOW. I'll be checking my hotmail account and it will happen. Very, very frustrated as the computer is 5 days old. It is a Windows 7 and I knwo very little about the specifics about computers. I have read some other posts and will try safe mode suggestions. If anyone has any other other advise, please help. I have not called either Qwest tech support ot the company I bought the computer from as I feel that they are going to say there's nothing wrong with their product, it must be Qwest or vise versa. But I will call today anyways, though I dont't think it will help.