1. IF he is kicking the 20 amp AC breaker, then regardless of the Microwave/wh on will NOT kick the 20 amp AC breaker, the MAIN breaker will kick
2. His description,(if the coils are clean) shows a defective compressor. OR the 3 wire terminals on the compressor are burnt and need replaced. OR,(the noise he hears at trip) is a loose 120 wire nut connection at the power source hook up at the main control. It is arcing and shorting out.
3. How old is the unit?
4. The board is a serviceable part but I doubt your board is defective. Doug