I notice that the entire drive select light, from PRND12, all are lighted up and

Assuming you have a 2 wheel drive A4 (not quattro) it more than likely needs a CVT control unit. The unit is a very common issue that requires draining the CVT trans, removing the rear cover and installing and coding a new control unit. The CVT transmission also could have mechanical issues as they were not that hardy. A scan of the ecu with a VAS 6150 or at least Vagcom should pull up a fault for range switch or similar. Hope that helps.