I have looked at the videos and I understand what is happening.
It looks like everything is ok with the key, eis, and esl, and I am not convinced that the problem has anything to do with the drive auth system.
The fact that this never occurred until you did the conductor plate is what concerns me. If you haven't already done so, re-inspect the transmission electrical plug very carefully with a flash light. Make sure no pins or sockets are bent or pushed back in the connector and inspect as much of the harness as you can see under there for obvious damage. Make sure you plug back in everything you have unplugged on the entire vehicle before proceeding. If all that is ok, try to turn the key in the ignition and hold it in the start position for 5-10 seconds and see if the starter will run.
I noticed in the video that when you bridged the starter relay and turned the key on the starter was cranking the engine but the tachometer needle was not moving. This suggests a possible problem with the crankshaft position sensor, its plug connection, or wiring.
In theory, you should be able to turn the ignition on, position 2, then bridge the 87 and 30 terminals of the starter relay and that engine should start. Note: looked like you bridged 86 and 30 in the video to get it to crank when the key was turned on.
Hook up the star diagnosis, go into ME2.8, actual values, look at engine speed. You should see 200-300 rpms when the starter is turning the engine over. If there is no rpm value, you need to try a crankshaft position sensor.
Note: Because the tipstart function relies on the rpm signal to know when to stop cranking the engine, a bad sensor can cause a start interruption.
Usually you can just hold the key in the start position and it will keep cranking.
Check it out and report back