Could be a couple of things. If you have a friend with a car you can borrow stuff from to try & eliminate the possible problems it will make it easier. This is the order I would use to eliminate possible causes. You said it isnt the battery so I will skip that as first step.
1st, plug your receiver battery directly into the receiver to bypass the switch. If it works your switch is dead.
2nd Try a new pair of crystals in the transmitter & reciever.
3rd Try a new receiver, you dont need to pull anything apart just unplug your servos from the one in the car & test the new one before doing a full instalation.
4th Try different servos, again dont install just plug into the receiver & see if they work. (unlikely this is the problem.)
5th Try a different transmitter.
Other than battery these things is all it could be. Good Luck