Disconnect the wiring to the low pressure switch. Take a short piece of wire and trim back the insulation some on each end. Basically, you're going to build a jumper wire. Start up engine and activate A/C. Stick one end of the wire in one side of the low pressure switch and the other end of the wire in the other end of the low pressure switch. If the clutch engages, either the switch is faulty or the refrigerant is gone. Only allow unit to run long enough to see if clutch engages. If system is dry you could damage it. I do realize you charged it up, just trying to cover the bases.
Before doing this, fire up the car and see what happens after the belt has been replaced. 103 belts like to be snug. You mentioned the A/C worked today. I doubt it's the pressure switch.
Time for the 4th!!!