If all your connections are correct, you need to do the fault finding part by part

1) First plug the battery direct into the RX and see if that gets things moving. If so you have a bad or badly installed switch or atleast a broken cable in the switch wiring

2) If that doesnt help, find a buddy who has a working pair of TX & RX. Put that RX in your airplane, connect and see whether whether you get a response with his TX. Then put your RX in his airplane and see whether you get a response with your TX. If you do get a response with his TX and RX in your airplane and not the other way around, there is a TX-RX related problem that you have

3) If that doesnt get a response either way, try to put in your buddy's battery. Sometimes batteries show 100% charge only to drop down to zero when loaded

If all of this doesnt help, the problem is deeper and then you will need a club to look at it.

I dont know of the compatibility between an Airtronics TX and Tower RX though

Ameyam