Anti theft?

Where were the wires that were chewed and wire colors if possible. It may be that they chewed through a wire that powered the body module and erased the memory of the keys, or there are more wires chewed through that you haven't discovered yet.

Put the key in and turn it, any dash lights or activity at all? Does it crank but not start? Red wires are power to the PCM as well as to the coils and injectors. If you have power and it does react to the keys you might try programming them in and see if that works. Usually though it will give you a warning if it's key related.

It isn't quite that simple. First you need a dealer level scan tool. You need to use it to check for any codes in the SKREEM and then reset it and verify that the PCM recognizes it. Then you use the scan tool again to add in the keys and fobs. Chrysler didn't make it simple to do.

A shop that has a scan tool and programming set up and that can use the Chrysler software can do it. They are one of the worst for this type of work.

Not on a Chrysler. They are integrated into more pieces so there is no good option. If you replaced modules and the light is still on there is still a wiring or hardware issue. What does it do when you try to start it? If it's doing nothing IE it doesn't turn over, that isn't the anti-theft, it is in the starting circuit. The light could be on because it simply isn't seeing power to a circuit that is also part of the starting circuit and the SKREEM in the column. These are the starting circuit. Use a test light to verify power and grounds for the module. A quick way is to use a scan tool, go into security and then see if it shows the key position and the security status.

No the starter wouldn't cause the light to be on. You said it worked ok until the mice chewed on it? Go over the wires you repaired and maybe take a picture of that area. Also look for missing wires, I have seen mice damage where they actually ate the wires right up to a connector so it looked like there wasn't supposed to be a wire there. List the wire colors and we can see if there is something missing. Also might be a good idea to take a test light and check all of the fuses. There seem to be a lot of failures in the fuse boxes themselves where the fuse itself is good, but it actually isn't connected in the box due to corrosion.
In this case a simple test would be to connect a test light between a ground and the yellow wire on the starter. Turn the key, the light should come on. Even if the anti-theft is on that should still work. If not then there is still an issue in the system. Might be a failed SKIM in the column. However I would start at the damaged wiring and look up the colors and what they feed.

No light = no start signal from the relay. Now you need to go to the TIPM and find the relay trigger wire (Dark green with orange in pin 11 of connector 1) that comes from the starting section of the BCM. It goes to ground when the ignition switch is in start. If you have that but no starter action, there is an issue in the TIPM. If there is no signal there then you need to use a scan tool to watch the network, with that you can see if the SKIM module is sending a start signal to the system.

A simple code reader won't do it. You need one that can access all the modules and that has bi-directional control.

There are several places. Topdon, Launch, Autel all make units that work like the OE StarSCAN system. They are not inexpensive though. Plus the issue on Chrysler products is that they can be a pain without the OE tool. The flip side is that the aftermarket system will do multiple makes and models. The OE tool is limited to Chrysler products. Price wise the tools that can do what you need are in the $1,000.00 and up range.

Let us know what happens and if you need more info.