My recently-acquired (last Feb.) '05 4Motion Wagon with AWM engine and Tiptronic (B5 #5 for me) recently began suffering from symptoms I've seen described here quite a few times: the starter would intermittently fail to energize. The solenoid would click, but it would not move far enough to engage the starter pinion or supply power to the starter motor. Jumping initially apppeared to help, but this turned out to be random coincidence.
My sequence of replacements was battery (it really did need this), starter (the one that came out is fine), and ignition switch. After the first two replacements, the car would start for a period of time, at which point the symptom would return. IOW, the parts I replaced had nothing to do with causing the problem. The third replacement was the result of a thorough troubleshooting process that involved much study of the wiring diagrams in the Bentley manual and jumpering across interlock relay contacts to eliminate them as causes.
It was clear from the symptoms that a contact closure, while reliably making, was intermittently resistive enough that the solenoid could not draw enough current to energize. Eliminating the relays left only the ignition switch. After replacing it - the OEM part was $60 at ECS Tuning - I took apart the one I had replaced in the hope of finding a smoking gun. I believe I found it: the switch contacts are reed types, in which all the force required for contact closure is provided by a spring (reed), in this case U-shaped copper strips with welded-on contact points that appear to be nickel-plated. This type of switch can become intermittent, even in very low-current applications (e.g., the pickup selector switches in Gibson guitars). The contact points for starter actuation (50b) were pitted and blackened from arcing, whereas all the other points were pristine. So far, two weeks in, the car is fine. If the problem recurs, I'll update this thread.
Knowing what I know now, I would go for the ignition switch first upon encountering these symptoms. The VW/Audi replacement part is not expensive, and the job is clean and only moderately involved (much cleaner and less a PITA than starter replacement). I hope this information will be helpful to others.