COMPRESSOR WON'T TURN OFF - Frigidaire FAM157S1A Air Conditioner

To clarify, the compressor and fan will run in defrost mode. The compressor and fan runs to dry out the air blowing onto the windshield.
Now if the condenser fan runs in "heat" you may have a problem with the fan relay or the main controller.

The key is the last part of the video, the part that wont move is unloader valve. The pressure switch under the lever is sticking and not allowing the switch to close.

you don't connect it up direct unless you want to destroy the compressor and burn the motor out
check for a reset or thermal overload button if it just shut down when over pressured
replace the pressure control switch is the best fix after checking out the motor condition

The leaking heater core won't keep the compressor from working.
You say the ac system is charged, but the compressor won't come on ??
The compressor has to run to charge the system, otherwise you will only get half a can of freon to go in. The system holds 3 or 4 cans when empty.
The low pressure switch has to be jumped to make the compressor run to take the first two cans of freon.

the compressor will turn on when freon is added a low pressure switch shuts it off to prevent damage to the compressor

Could the on/off switch be shorted? Could check with a volt/ohm meter, or remove and replace.

All compressors run up to their rated high pressure level, usually listed on the data plate on the compressor or in the manual, then the pressure regulator turns them off. If your compressor is not shutting off it is either not getting to the pressure it takes to get the pressure regulator to turn it off or the pressure regulator is broke and won't turn the motor off. To check which, turn the compressor on and watch the guage that shows tank pressure. If the pressure rises then stops at a level below the rated pressure for your compressor and the motor continues to run, you have a leak somewhere. It could be the tank drain valve, the lines from the pump to the tank, the valve plate or in the piston cylinder area. If the pressure rises more than ten psi above the rating for your tank, your pressure regulator is broke or possibly set too high. If you know how, you can try lowering the shutoff point to see if that fixes it but you're usually better off replacing the regulator.

Motor start capacitor probably bad.

Check the compresser relay?? Hope this helps?

Most likely a loss of refrigerant ( freon ) in the system. The A/C compressor uses a low pressure switch as a SAFETY to insure it wont turn on without freon in the system. Hope this helps.