brown tab of the headphone ribbon cable connector

I have heard of people using tape to hold the headphone jack cable in place with varying degrees of success. Usually the only way to fix that problem is to replace the logic board.

Sometimes you can try to place the brown tab back onto the terminal and still get it to lock into place. The most common problem is for one of the clips on the side of the tab to break off. The tab will still lock onto the ribbon cable even if you only have 1 of the clips intact. It's kind of a pain to try and position the tab and put it back on but it can be done with tweezers and patience.

Your other option could be to try and place the ribbon cable in the terminal and try to secure it with tape. I would try to put something very small (and non-conductive!) in the terminal itself with the ribbon cable thus pushing the cable against the wall of the terminal. Then you can try to tape that into place. A small folded piece of tape wedged in there should so the trick I think.