Since all the speakers always come on for the first few seconds every time you start your X, it doesn't sound like a corroded connection. If you shut the X off just after all the speakers other than the door stop working and immediately start it back up do all the speakers again work for a few seconds?

__________________
X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas