External temp reading -40 degrees

Forgot to add that the headlights, signals and horn randomly work. Stereo is fine.

You need to replace the Ambient Temperature sensor. Its usually mounted behind the front grill or bumper, looks like a black square with a nose on it. Not surprised, police cars go through a lot of rough-housing. Start by replacing the sensors that are giving you issues, then work your way back. Worst comes to worst, you may have a serious electrical issue that can be shorted virtually anywhere from the ECM to your grounds...unless you feel like tearing apart the car, cut your losses and sell or just drive as-is