I have a 5DM3 and recently found my joystick at the bottom of my camera bag. I pressed it back on but it didn't work properly.
So I found a reputable registered repairer and sent it in.
The repairer told me that I shouldn't have pressed it back on myself and the back of the camera has to be pulled off, in order to repair it. The repairer said that with these joystick issues sometimes the whole back of the case has to be replaced.
I was lucky, nothing was broken and needed to be replaced.