For what it's worth, I keep my joypad perpetually plugged in, and the rest of the system doesn't have a problem with it.
...now that I think about it, have you considered reinstalling DirectX? DirectInput may be damaged in some way, and that is the section that governs the game controller aspect of the computer.
But before doing that, boot up DXDIAG and go to the input tab, and see if it sees your controller and/or reports any problems with it.