I had a similar problem, but with Windows XP. About two months ago I was restoring a friend's computer. It was an older Gateway desktop. Turned out it was a driver issue. I used the driver that Microsoft provided through Windows Update instead of the driver that came on the Gateway driver disc. When I restored the system for the second time, I used the Gateway driver disc first, then applied updates from Windows Update and never had a problem.
For what it's worth, it was all six ports - 4 on the back and 2 in front - that caused the issue. If I plugged in anything besides a keyboard and mouse, the computer just shut down immediately as if I pulled the plug.
You might try getting a powered USB hub for < $30 and plug it into one of the good read USB ports. Otherwise, if it is a new purchase, I would return it or tell the shop where
you got it to fix it. If you still have a warranty, they should cover it. They should search for the fix for you since you are the customer.
Good luck!