Desktop Shuts Itself Down

So, I have a fairly new Gateway LX Desktop, and yesterday it started shutting itself off at random, about every 15 minutes. i try rebooting, but it still does it. I tried downloading Avira to scan my computer for viruses, but it shuts itself down before I can finish the scan. I honestly don't know how it started doing this out of nowhere, but I need my computer to be up and running. Geek Squad is trying to charge me around 100 bucks to remove a virus, if that's what it is. any help would be appreciated.