Not using steam, just checked the error logs in the binding file and its saying there is no gamepad detected, while its plugged in and working.
Windows update does all kinds of wonderful things to peripherals, up to and including resetting registry entries for them.
Is the controller present in the joy.cpl applet?
Back up your current binds file and start a new custom one with a couple of entries in the axes. Them open the binds file in Notepad and note down the ID used by the game. If it's a different ID, that's your problem. This can also happen if you move the port the controller is attached to.
If that's the issue, you can hit Ctrl+h and do a search and replace for the IDs in your original binds file, replacing the previous ID with the new one.
Edit
I see you fixed it. With the knock-off Xbox controllers, you have to force them to use the Windows Xbox controller driver. As the controllers aren't actually Xbox controllers, Windows refuses to use the driver automatically, giving you what seems to be, basically, a worthless controller.