IF you can wiggle the whole jack then that means that the internal structure of the port could be damaged. If thats the case, then the issue isn't with the connection on the outside, but with the solder joints connecting the 3.5mm jack to the board on the controller. [br]
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You can try following the teardowns on the site and carefully inspecting the port once its apart. If you see any legs of the port are not connected then you can try resoldering it.