Okay, a few more things to check. Make sure the engine is running and the A/C is switched to "on" inside the car.
- Fuses. 7.5A #13 in passenger fuse box, 7.5A #3 in driver fuse box, 20A #58 in engine fuse box. #13 controls power to the HVAC controls, #3 controls power to the compressor relay, #58 controls power to the compressor clutch. If any are blown, you've got a short to ground somewhere in the wiring, which I'll help figure out if need be.
- There's a compressor clutch relay in the engine bay fuse box. Try tapping it with the butt of a screwdriver, see if the clutch engages.
I would place my bets on the relay, the next most likely place would be a broken power wire. Grounds should be okay since you can jump power to the clutch and it works. I'm gonna go ahead and say that the pressure switch and the evaporator temperature sensor are okay, since if either of them were bad the A/C request signal wouldn't get sent from the HVAC controls to the ECU (this is what is raising your idle).