On the plug, despite the damage to the coil, the voltage should be. On the compressor you should have the name of the producer, as you can check and give it to the table. I will sit down and describe the principle of operation.
Added after 3 [hours] 22 [minutes]:
Check the fuse F31 15A inside the vehicle should be powered after ignition, it supplies the air conditioning compressor relay. It is very important that the three-pin high pressure sensor is okay because without it nothing will start. Check fuse F52 and F53 30A in the engine compartment they are responsible for the work fans. From the air conditioning switch goes the signal wire to the body electronics controller has a white and black color from there, through the bus can communicate with the motor controller which manages the masses of individual relays. The pressure gauge pressure sensor is also connected to it. It's so roughly and it is a description of the installation Hella. (Firstly indicated fuses and high pressure sensor to check)