I'd definitely say you have problem if the LED is not doing anything. Just had a peep at mine in the garage and the LED is slowly blinking at me to highlight the immobiliser is active.
Not something you note down but from memory when the key is put in the ignition and turned to ignition on; the LED blinks furiously until the fob is brought up close to the underside of the ignition barrel, the LED then goes out and the engine can be started. There is a time limit on how long before the immobiliser gets to see the fob, if this is exceeded then ignition off and try again.
But if you don't have a slowly blinking LED at rest with no ignition on, then you probably don't have a working immobiliser.
Steve
