How do you know you have the proper mass of refrigerant in the system? If the level is low, the LPCS won't allow the compressor to engage.
The clutch pulley should freewheel when the compressor is not engaged.
If you jump the LPCS, the compressor should kick on. Do not allow the car to run like this for more than a few seconds at a time. It does allow you to check the wiring and pressures, and introduce extra refrigerant into the system.
Good luck.