Maybe get someone to have a look through a diagnostics scan (VCDS) for you.
If you have some buttons at the base of the b pillar, you have an alarm, if no buttons, you just have an immobiliser. One of the buttons turn off the motion sensors and the other turns off the tow away protection, if you have these I assume you have an alarm. If no buttons, maybe an import.
Have you tested for an alarm? IIRC you lock the car with the fob, wait 30 seconds or so and unlock with the key and Roberts your dads brother, noise.