I quote from the Chrysler Crossfire Student Reference Book: "The Vehicle Theft Alarm system sounds an alarm, flashes the exterior lamps AND disables the ignition system when the alarm is triggered". There just might be a chance that the Central Locking Pump/Security System Module located in the rear of the vehicle is messing with you. It is easy to check if water has accumulated in the rear by putting a small slit in the rubber plug under the car on the passenger side and with a slight twist see if any water comes out. The plug is aft of the axle. It's easy and fast just to check. Might try pulling fuse nine too, can't hurt. Placing the key in the ignition system and turning it to unlock position disarms the system IF it is working correctly.
That's a lot easier than tearing any farther into the dash. May not be a problem either, but it is easy and quick to check.