The immobiliser is built in to the cluster on 99> facelift cars so you won't have a separate wire or immobiliser box, which is what I think the original post is referring to.
In the facelift cars the wiring is just part of the main dash harness, but not immune to problems - usually its the small black plug in the reader coil attached to the ignition barrel. That is either loose or the connections aren't tight enough on the pins. Sometimes it's enough to just pull the plug and reconnect it. I had an A4 in which had the same symptoms but if you thumped the column it would start right up. Re-seating the connector solved that. Just picked up a TT with a similar problem too so will be investigating that shortly.
Not sure whether the D2 has the same reader coil as the other models, as thats one of the few areas of mine I haven't taken apart yet and I can't remember from the last one I had in bits. Maybe someone else can help on that
