PCM problems?

Did you post a reply? I did not load correctly.

Okay, then it's most likely malfunctioning, and yes it can cause a battery draw. Unplug it, it looks like it's just put in series on that pink/light blue wire, they just cut the wire and put the device in series so they could disable it if needed.

Take the box out, reconnect the pink/light blue wire that should take care of it.

Does the vehicle start? The power and ground doesn't unplug from the box?
This isn't a fusible link, it's a Ferrite Core on the wire, they are for suppressing low-frequency noise and interference.

The black wire is going to a body Ground and the red wire is going to a constant Battery Source. The current draw on these devices is 50ma, so that plus what the vehicle already pulls for amperage when asleep can cause a battery to go dead. Now the device is obviously malfunctioning so it might be shorted out inside pulling more amps. Cut the black wire first leaving a small section, just in case. Then cut the red wire and cover the red wire with something so it doesn't short out on anything. These things are pretty expensive actually. But this one is no good. The black and red wires are actually on a connector going to the box, you can unplug it also, but it will be a live wire, so it needs to be covered over. I would cut the black ground first though so there is no more current flow before cutting the red. If you want, put a meter lead on the red wire and one on the battery positive set on DC volts, it should close to 0volts. In the installation instructions they have it hooked to a constant battery source so whoever installed this thing could have tapped into anything due to the low 50ma working amperage.
If you're going to through it away after this, I will take the module. The parts on e the circuit board inside can be used to repair other vehicle modules in the future.

It's kind of strange this thing has been in your vehicle for that long. Did you buy it from a used car dealer or a Chrysler dealership?

If it's a grey key that is a Valet key. They don't include a transponder in those keys.

Is it starting okay without the box hooked up?

Okay. Well, this OEM diagram shows that power to Fuse 23, 26, and 32 come through the ASD relay, and it would have to be energized for that to happen. Do you have power on Fuse 18 40-amp? Thats what feeds the ASD relay. I don't have anything in these diagrams that's labelling 30, 87, 85 and 86. This is the OEM diagram too.
There should be constant power to the ASD relay, so I would check the underside of that fuse panel for any possible broken pins.

I don't think it should crank when you jump 30 and 87, Is that with the key on? Or is this just happening when jumping the relay.

85 and 86 are the two relay control pins, and 30 and 87 are the load pins. Technically speaking Fuse 4 10amp feeds the Ignition Switch which then in turn sends power to the Starter Relay with the Switch in the Start position, then the PCM grounds the Starter relay at the same time which will then send power to the Starter motor.
Does the Check Engine light come on as well? Something doesn't seem right here,
Is your battery voltage still low right now?