I’m assuming that the opener’s motor doesn’t respond at all after the last half-travel and reverse: “When I push the wireless remote I hear a click form the power unit but nothing moves, the motor doesn't make any attempt to start.”
Some of the units are equipped with a safety lock feature but according to the manual this one requires an extra wall multi-function control (it’s basically a box with 3 buttons – page 30 of the manual, bottom / left corner – model 57LM) for the function to be activated. This feature blocks opener’s activation from any of the remote control units and from the wall push button and it is usually annouced by a blinking LED light.
It may also be the motor itself, they do fail / burn over time as well and since this one doesn’t respond at all (except for the relay clicking noise) this might be just it. If the unit hasn’t been accidently locked you may need to call a professional for troubleshooting or install a new garage door opener.
Just keep in mind that purchasing / replacement of broken parts (electronic board, motor) in an older garage door opener
might be more expensive than getting a new one.