This sounds similar to what happens to me if I start up my WoW and exit before I realize that my gamepad is connected. You see, for some reason, when initially connecting gamepads, especially those with analog axes, you need to start up a game that recognizes the pad (in my case WoW), and on the dpad do a circular motion a few times, and press all other buttons a few times, and then the system finally sees the x-y "range" for each button press and voila, no more stuck button.
Until you do so, you'll end up with a gamepad connected whose buttons are sensed as being at one extreme or the other of the x-y button press range values and thus is "stuck".