Oh, moving the steering will power the Rx, that makes sense now. Anyway, check the cable, if it's not that, probably fried internal BEC in the ESC.
This is why you gotta have multiple RCs, so you can mix n match for troubleshooting purposes :)
If you say so. It works fine, only you don't know if it works fine since you can't drive it.
The fact it generates voltage output on the BEC side when you move the wheels is also not really normal behaviour.
Sounds more like dead ESC to me. Or at least the BEC in it. Get a voltmeter, or a 5-6V bulb or LED and see if there's any voltage output on the ESC (the cable going to the Rx, which powers the rest of the electronics).
The ESC should output 5 or 6 V (most commonly). It powers the receiver and...