You may get better luck over in the TJ section. I'm sure one of the folks there has experienced it. The a/c systems in the JK models are different.
We would need more detail anyway such as do the knobs move ok, just nothing is changing within? Sounds to me like a vacuum issue but I would not know where to look on your model.
2007 JK Wrangler Unlimited (Black), 4" SuperliftRanchoExpress Lift, 36" Super Swamper Irok's covering 16" ProComp's, AFE CAI, FlowMaster 40 Series, Shrockworks Rock Sliders, Rock Hard line of undercarriage skids, Warn Powerplant, Shrockworks Mid-width front bumper, Dana 44 Front