If you are running an older version of Windows, you may need to download and install the driver for the controller.
You could try different USB ports on the computer as well, perhaps ports in the back to make sure the issue isn't with the front hubs, assuming that is what you were using in the first place.
This could lead you to obtaining drivers depending on your Windows version (directly from microsoft):
http://support.xbox.com/en-US/xbox-on-windows/accessories/connect-xbox-one-controller-to-pc
Best of luck!