I have an A4 (2000) Jetta that has plagued me for a couple of years with an immobilizer problem. It happens randomly, about 3-4 times a year. I have tried everything...reprogrammed keys, new keys, disconnecting the battery. Nothing has eliminated the problem. But, it is so intermittent that the dealer cannot suggest anything else except to begin replacing things (from the sender in the steering column up to and including the main computer). The first few times it happened, I had the vehicle towed to the dealer. On each occasion, the car started up fine when they tried it, even though it would stubbornly refuse to run even if I tried it over the course of several days. Even if we tried replacing components, I would not know if there was a fix until some months later if the problem arises again.
The only thing that has worked when this happens is to turn the key to the on position and wait. The immobilizer system on that vehicle will give up in anywhere from 10 minutes to 60 minutes. When the problem is occurring, there is a dashboard light in the shape of the key that flashes, indicating the immobilizer system is preventing the car from running. (It starts, but the system shuts off the fuel pump after about 1-2 seconds). After the light stops blinking, the car will start like nothing happened. After that, you can shut it off and it will restart just fine. It will operator normally for months before it happens again. You have to wait until the light goes out. If you try starting before that happens, the wait just starts all over.