I don't think the click sound is coming from the compressor. I belive the click is from the solenoid or relay engaing. It appears that a relay or solenoid is engaging to start the compressor, but the compressor never kicks in.
do you have a volt meter and know how to use it?
I sure do. I am a degreed Electircal Engineer :-)
No problem. A service repairman came and fixed it. It was a bad relay. That was your original diagnosis so i will accept and pay you.