The speakers are in the top half so after you check they still work at some level and have not come loose or something then I would look at the ribbon cable and such. In the hinge.
The game recognised or not is probably unrelated. Check the condition of the slot and make sure there are no bent pins or foreign items. After that you can clean it with some contact cleaner. It is not unheard of for slots to break (indeed it used to be a reasonably common thing to swap out) so you can replace it if you want -- it is a fairly involved soldering job though one I would expect most reasonable surface mount soldering types to be able to do.
Disassembly is usually a matter of screwdrivers, ribbon cables and maybe a spanner if the hinge is that far gone. No particular springs or crazy hidden screws, welded seams or short ribbons that will break if you take it apart in the wrong order. Not an entirely trivial disassembly but nothing drastic. Still has a step by step.