If you have the same exact problem as I had on my 2002 A4, then I have the remedy!![wrench]

SYMPTON'S:
-License plate lights dont work, no power to them at all.
-Trunk won't open unless using the key to open.

I discovered 4 wires completely cut in the wiring loom/boot that protects the wires exiting the trunk to the trunk lid.
I assume over the years of wear and tear, and the extreme angle, they finally completely broke at some point.

Check out the picture showing the location of the damaged wires. I spliced in new wires and both problems have been fixed.