I found this on another JK forum. Might want to try and give it a shot and let us know what happens.
This sounds like an issue with the WCM (Wireless Control Module). It is mounted under the plastic behind the steering wheel between the dash and the wheel (left of ignition key hole). It controls the remote key entry (RKE), ignition key programming and remote start. There's also an antenna that connects to the WCM. The cable could be lose or shorted. I would first try to reset it and see if that helps.
The WCM can be reset by either: disconnecting and then reconnect the battery negative cable at the battery, or by removing the IOD fuse (with the key out of the ignition switch), waiting 30 seconds, and reinstall the IOD fuse.
If a reset doesn't work, only a dealer can replace the module. The ECM and all keys have to be reprogrammed when the module is replaced or the Jeep will not start. It is solid state and susceptible to static electricity that can travel through the key when inserting it into the ignition.