Joystick signals always upwards, even WITHOUT a joystick in case?

Bought a 3000 off of Ebay. The analog joystick seemed to be faulty, because in every fps game the character moved full speed ahead without me doing anything. I change the joystick, same behaviour.

Now disconnected the joystick completely (there is a hole now where the joystick is supposed to be) and STILL: every game behaves as if the joystick in a constant upwards direction.

How can I even begin to fix this?