While the lid is off I would be tempted to burnish the pins, or at least scrape them a bit. Then I would have a look with a meter for the voltage turning up where expected - there should be battery voltage across the servo power pins, both with and without the servo connected. If the voltage is there, that leaves the signal pin. As the signal switches rapidly, all you can expect is a messy reading. I have been caught a few times by dry joints/hairline fractures in the tracking at or near the pin base. The dry joint can be cured by re-soldering, the fracture by cleaning the track and soldering a short length of wire over it.
If the problem is any deeper, it really isn't worth looking further as you are then into the area of either parts that you can't easily get, or can't replace without wholesale destruction, and a new RX is then the answer.
