The black box that the transponder ring plugs into is the DAS box. This takes the code from the key, if it matches the code in the box, it then sends a signal to the engine computer to turn on fuel. The DAS box also sends a new code to the key for the next start.

There is a white connector with 2 green wires that plugs into the DAS box , this is the CAN bus communication wire that lets it talk to the engine computer make sure that is plugged in.

To resync the remote locks, point the fob towards the IR receiver, press the button 2 x , insert the key in the ignition and turn it to run. The 2x press alerts the IR lock system that a new key is being set up and turning it to run verifies that it is a real key not a hack. I'm not sure if the DAS issue will prevent registering the key.

I'm pretty sure if you unplug all 3 plugs from the DAS box, the car will start stall rather than just not try to fire.

If you get parts as a test, you need a key / DAS box / engine computer all from the same car. Mix and match won't work.