R/C Tech Forums - Need help understanding compatability of recievers and transmitters

My granddaughter gave me a challenge this past week when she handed me a beat up Art-Tech Cessna 182 that she picked up at a garage sale. She asked if I could fix it up for next spring so we could fly it together. Being the fool that I am I said I would try. Although I could probably buy a new one cheaper than fixing this model, I have the time and it is a bit of a challenge for fix up and learn about the various parts.

I think I now understand the mechanical problems and how to repair them (including replacing the battery ESC and motor) but I am not sure if the existing transmitter and receiver actually are a match. The servos operate when voltage is applied to the receiver and the receiver reacts to the transmitter going on and off but none moving the controls on the 4 channel transmitter seem to impact the movement of the servos.

Is it possible to put a new receiver in and drop a matching crystal in the existing transmitter or will I need to replace both receiver and transmitter? Is there a place to learn more about this compatibility problem?