Car battery completely dead - Caused the Key to be stuck

Your key is stuck because your battery is dead, try hooking up a battery charger to it, remember to pay attention to the proper battery terminals so you do not damage your battery or your electrical system.
The key is likely stuck due to a solenoid that is designed to keep you from removing the key if the vehicle is not in park, when the battery is dead the car does not know it is in park and therefore locks the ignition tumbler from returning all the way off.
How To Connect Battery Charger

I'm not a car mechanic, but, it sounds like you might want to check the fuse to the ignition switch, and, if that fails, it might be a problem with the Start Safety Switch on the transmission. Good luck.

Check your fusible links by the positive battery cable.Here's a link to it.

Raise the car up,support it in the front

Put a battery charger on the battery cable
at the starter and the ground to the sub frame

Charge the battery for a couple hours,then try to
open the door with key fob

If the battery is completely dead you should buy a new one. Batteries get damaged when they completely discharge. Just put in the new one and start. You might have the emission light go on after a start from a dead battery. Reset it yourself with an OBDII tool or your dealer can reset it. You can drive there at least on your own this way.

I have had the same problem with my daughter's car. She inadvertnetly left the key in the on position and the battery went dead. Apparently an electrical current is neded to withdraw the key. I put a battery charger on the car for several hours and everything worked fine after that.

Is this still being used as a patrol vehicle? Still has a laptop charging station and all that junk? You need to do a parasitic draw test. Do you have an ammeter?

Check your alternator

just clean and tighten your battery terminal connections, both positive and negative poles.

Look at the battery cables. Sometimes if the ground wire is loose, it wil display the same symptoms that you have described to me. If they are tight and free of corrosion then look towards the ignition relay or key switch. Key switch would be a likely candidate. Keep me posted please.