I had a similar problem with both a wired 360 controller and a wired 360 joystick. I closed all non-essential processes in Task Manager and tried both IE and Firefox. Eventually one of these things got it working, all I can say is keep trying stuff

I had this problem for two or three weeks and it fixed itself somehow. I wish I could tell you more than that. Perhaps try System Restoring to the last date that it worked?