Transmission problem Audi A8 , reverse gear problem

Hello to everyone, since I have been looking for the wolf on the Internet for the solution of my problem, I am looking for help here resp. Tips. I made a real snapper 2 months ago, a nice Audi A8 4.2 Quattro automatic / Tiptronic , almost in new condition, as it was a driver's car, only 128,000 km running, top maintained, first hand, EZ: 01.04.1996, transmission identification letter is CML engine identification letter : ABZ. The car was in the garage for a good two years before I bought it, it was not moved, before everything worked perfectly. I've read somewhere the gearboxes don't like it at all. Therefore, the only hook on the car, he drove and does not drive backwards. Had tried a little bit to make me smart on the net before, but there is not all too much about the A8 and a lot of different opinions and diagnoses. But maybe someone here has a plan? So how does that express itself?
Forward the car drives perfectly, the gearbox switches softly, without cracking, or jerking. If you start the engine in P position and let go of the brake, the car rolls for a short moment, but then stops. If you insert driving level N, the car drives in idle mode (cannot be accelerated ) in D position everything normal, runs like a 1, without problems. If you then insert the reverse gear, the gear goes in, the rear light lights up, but the car doesn't drive backwards, nor does it pull on when switching, so it's like when the gear is neutral. I've already read AutoDia, not a mistake.
Well, I have now searched through many posts on the web and many guesses, from slider box, via electronics etc. but no one seems to have such a real idea.

So I am grateful for competent help / tips, respectively. for addresses of transmission specialists, preferably in the north, which offer a reasonable price / performance ratio.