I might say here that when trying to diagnose problems with a sophisticated machine like this(especially the tranny), the $25 spent to get a subscription to Alldata.com would save soooo much heartache for soooo many..I wish everyone would start with that. They have a programmed approach to solving codes, otherwise, you just guess, and often you guess wrong. In general, code descriptions are written in shorthand and are not meant to be the problem solving key, you have to have the BOOK.

 

Generally speaking - you are correct - 17125 could be caused by everything you stated (following the troubleshooting chart from ElsaWin, correct?)
Audi addressed the issue in TSB 32-05-02 and TSB 32 07 01 Jan. 18, 2007, 2010879/9.
The solution is TC replacement.
This is one of the major VAG’s failures and justifies a class action to get to the point of recall and compensation.
An evidence of design and workmanship inferiority never addressed openly by VAG – one of the many occasions where VAG does not stay behind their products.(but who does?)