I took the GTI to Best Buy's auto installation department. They did a very good job on my Mazda, so I had some trust in their work. After the fuses were ruled out, using a really cool electronic tester, they discovered a third culprit. The head unit was getting power and there was power coming from the line, but in between the line and the head unit sits the PAC radio replacement interface. This unit allows an aftermarket stereo to use various VW controls, like from the steering wheel, but also allows for the various audio noises that come from the car, like door chimes.
The installer, a meticulous technician who gave me lots of good advice, was able to reset the PAC unit and get the stereo working again, but there was no doubt the interface unit was the culprit. While he was on the clock, I had him re-route the Sirius antenna to the roof from the dashboard. Hopefully that will fix my satellite reception complaint [it did].
When does a car become a hobby? I'll let you know.
I'll be working to get a new PAC unit from the original installers and then I'll go back to Best Buy. The installer will be re-routing my iPod cable from the glove compartment to the center console. VW already has an iPod cable in the center console, so it's a fairly clean install. I'm finding the Pioneer unit doesn't recognize the iPhone about half the time, requiring me to unplug it and plug it back in. This is a drag when it's in the glove compartment.