That's because your throttle also happens to be your power circuit. Without that plugged in, your receiver is getting no power. Your ESC has a BEC built in which powers your receiver from the main battery.
It's unlikely that only one channel on your receiver has stopped working. If you still want to try it, plug the throttle from your speed controller into a different channel, then plug a servo into channel 3.

In all likelyhood, something on your motor or ESC has gone. If you crashed the helicopter while it was under power, it's likely your ESC.

Smell it, does it smell like toasted electronics? .