Replacement #1: PIONEER OE CD CHANGER
Hint: This was not a good sign...

For anybody buying an E38, if the letters "CD" are not in the area circled above, you either don't have a CD Player installed, or its not working - or you (hopefully) have an aftermarket modified system.
I'm not sure about other model year E38's (95, 97, or 98), but the 1996 takes a very specific Pioneer model. I learned the hard way...
The dealership I bought the car from said they would replace the unit for no charge -- cool. They had it for a day, and then told me they had ordered the wrong changer. Okay.. still no problem. Two months later, no unit... Problem started.
I resurrected the issue with the dealer by offering to help "locate" the right changer. They said, "you get it, we'll cut you a check, and we'll install it." I contacted Circle BMW, based upon some good feedback from the E38 message board. They were prompt in sending me a changer for my 1996 E38.
Being very calm and reserved, I tore into the project. It literally takes about 10 minutes to do a complete install. Piece of cake - the changer had two wires and I saw their component wires lying by the amplifier. You can see the wires in the pictures here...

Here's the gut wrencher - you know, the part where you've hooked everything up exactly right, and even put the test disc and magazine in the changer. You can hear the changer checking all the discs - and you even see it saying so on the display on the radio. But, that doesn't mean it's working. After all, I didn't hear a thing.
Three times, install/uninstall/reinstall/unitstall/...you get the picture. I took it to my dealer. They told me it was not the correct unit. I called Circle BMW. They told me it was the correct unit. I called a local BMW dealership - Fairfax BMW. Fairfax gave me a totally different part number. I called Circle BMW and gave them the new part number. They said they had never heard of that part number, but found it and special ordered it for me. I packed up the first unit and sent it back to them.
Circle BMW sent me the second unit and I again tore into the project. In the picture below, you will see why the first unit did not work...

There is a 3rd connector that plugs into the changer from the amp. I saw the wire during the original install attempt (with the wrong unit), but couldn't figure out what it went to since the wrong unit didn't have female connection for the wire.
Anyway, all is good now, and I even have sound! - See my test disc below...

Yes, life is great again. I hope this experience can aid others in avoiding the hastle of the wrong OE changer. Below are pictures of the correct model and part number for the 1996 E38 OE Pioneer Six Disc Changer.

For the greater good - Circle BMW gave me full credit for the exchange, minus my shipping costs ($7) and $23 for the difference in cost of the new (correct) unit.