There is a video showing someone doing a repair of the connector here. Although the repair is for a different problem than the one you describe, based on that video, you should be able to get a fairly good idea of how to repair it.

From your description, it sounds like the keeper tab that holds the connector pin in place (the thing that, in the video, is being disengaged by a small piece of wire) has come undone. The repair might simply be removing the pin, bending up that keeper tab a bit, and re-inserting the pin.

By the way, you didn't say whether you had a Mk1 or a Mk2 player. The two players have different connector assemblies. If you have a Mk1, the repair will probably be a little different.