I had same with my frost free freezer motor still making a noise as if running but it clearly was not, the auto defrost must have come on as I heard a noise when it went wrong so switched on spare fridge/freezer left an hour for it to cool then started transfer and stuff at top had started to defrost. I was about £190 new, and they wanted £60 just to come out, repairs on top of that, I assumed motor from noise I heard and decided best option was a new one.
The clicking however could be the over current device. With any single phase motor the start torque is low, so the pressure needs to have equalised before it tried to start, if it has not equalised the overload trips and is designed to not reset until there has been enough time for the pressure to equalise, if there is a volt drop for example running with an extension lead, then the over load can trip an excessive amount of times, and they then fail. It could be the overload you are hearing. Normally renewable and built into the motor.
New fridge/freezer and freezer are both three phase driven with an inverter so that is no longer a problem.