You may have burned up the compressor motor, Roger, something that happens when plugged into park service with inadequate voltage. Keep in mind that a roof air requires you to be plugged into at least a 30 amp circuit, though on our old Pace Arrow I could run one on 20 amps - it was a bad idea probably, and you certainly wouldn't want to try to run the fridge or other appliance at the same time - if you're lucky a fuse blows before the motor. If the motor can't get enough voltage, esp. at startup, it has to work too hard and overheats, then it and you are cooked. That's why it's prudent to check the voltage with a multimeter or other device at the utility post before ever hooking up at a campsite; though that is not failsafe, since park load can change from minute to minute, and the available voltage at any one post with it. Newer well-engineered parks usually are less of a threat in that regard, but not to be taken for granted.
The click you hear may be a thermoswitch (indicates ambient temp. is a go for unit startup) or a sailswitch (indicates fan speed is adequate for startup) telling the motor to start, but it can't because it's fried. Replacement of the compressor may be necessary, and often people end up replacing the entire unit because it's just as cost effective.
I'd like to think that our modern coaches have protections against such threats as out-of-bounds park voltage, so perhaps your problem isn't what I described, or your built-in surge and voltage protection should be checked. I'm no expert, so others in the BAC more familiar with house A/C than me may have additional ideas.
-Joel