Check the socket in the dash where you press the immobilisier key into. In particular the wiring. I had a Meta immobiliser on mine similar to yours
Eventaully over time, the continual pushing in and out had caused the socket to twist, in turn causing one of the small wires at the back to become detached.
If in your case, it is not this, try asking a immobiliser/alarm fitter. Not sure you will be able to get those type of key anymore?