Hello and welcome to Just Answer,
Unfortunately, it sounds as if the access/start control module has gone bad. It is very common for the 05 model year, so common that Audi releases a technical bulletin for it a few years ago. The access/start module is responsible for recognizing the key and starting the vehicle, it also unlocks the transmission and steering column. The module has since been updated and there is also a wiring update to go along with the new module. The really bad news is that the access/start module is built into the steering column and must be replaced as a unit. Also, only the dealership can replace it as they have to reprogram the immobilizer system along with all of the keys to the vehicle. I hope this information has helped and if it has please click on the accept button as that is the only way I am compensated for my time and knowledge.
It depends on whether you have an electronically adjustable or mechanically adjustable column. If its electronic its about $825, mechanical is about $740 for parts. You then have to add about 2.5 hours of labor at you local dealers labor rate and finally you should have an alignment done at the same time. Worst case scenario at our dealership located in Lancaster, PA would cost you roughly $1300. I hope this helps, I hate to give such bad news so close to the holidays, but try to have a Merry Christmas if you can.