The concept to my replies were to give info for the evaluation of WHETHER it IS the PBC or the Klima. I'm not going to read back through this its your car.
The story IS: the PBC does ONLY one thing in this reguard; it grounds the Klima on the circuit that the low pressure switch is in. (so convenient for testing) Quit thinking about the low pressure switch (you now know that you have pressure). DOES THE CIRCUIT GO TO GROUND WHEN A/C is called for at the PBC? It either does or it doesn't.
DOES the Klima turn the A/C on when that circuit is grounded????? (easily done at the low pressure switch). This whole decision should be verifiable in a minute or two. This is simple stuff!!! Either the PBC doesn't switch the Klima to ground or the Klima doesn't respond when switched to ground. No more complicated than a brake light.
You, no longer, should have any reason for not knowing whether the problem is a dash decision (PBC makes the inside decision) or an engine decision (Klima makes that decision). This job starts with making that decision once there is pressure.
Bosch Master, ASE Master, L1
33 years MB technician