This model has its AirPort board located in the center plastic clutch cover between the hinges. It's a fair amount of work to get to (heres the IFIXIT guide: [guide|6019]). From the sounds of it you may need to replace it.
I would start off inspecting the cable connection on the main logic board which you can see in Step5. You might want to re-connect it so the contacts are making a good contact. Make sure you don't have any liquid damage on the logic board.