Would be nice to know what, if any, DTCs are stored in the instrument cluster.
I will put this on the table... a common problem with the Immob2 and Immob 3 Beetles, aside from the fact Magneti Marelli can't make instrument clusters... the wiring harness for the instrument cluster uses Insulation Displacement Contact(IDC) terminals. So instead of stripping the wire and doing a mechanical crimp onto the copper wiring (good), the wire is cut, but not stripped, and then the terminals have points that are suppose to cut through the insulation and make contact with the copper strands (bad).
To that end, this can lead to a poor electrical contact between the wiring and terminals. On the green connector of the instrument cluster, terminals #2 and #17 (black and green wires) are for the Reader Coil (D2) of the immobilizer. The poor electrical contact of the IDC can screw with the signal or data from the key to the immobilizer, thus the immobilizer says, "Nope".
If you pull the 2 wires out for the reader coil, you can use a pair of pliers to close the gap on the terminal where it is biting into the wire.
|_| Go from that, to this /_\
You only want to tweak on the part biting into the wire, DO NOT MESS WITH THE FEMALE PART!
Normally when this is an issue, you will get the following DTC:
01176 - Key: Signal too Low