I have my reservations on the ISO connector. The Avic D3 had 2 connectors, did you also get 2 ISO connectors? Can you return the connector and put the $ towards a better connector? I's also ask the guy that you bought it from about the issues.
When you disconnect the blue wire it turns off the amp and the sound goes away because the amp is off. Now I'm wondering about how the head unit connector (ISO) is grounding the head unit. Yes, the thick brown wire is a ground.
My recommendation is to contact trieullionaire and purchase his connectors should be just a few bucks. He also includes some great instructions that you can pull down from this thread, etc.
http://986forum.com/forums/showthread.php?t=15893
Trieu might also have some ideas but basically it's a ground loop issue and I'm stumped on the configuration of your ISO connector.
Puzzled...
-Steve