I have a similar problem, the key fob doesn't work. I have replaced both the GM3 and the antenna modules with a new ones. Still can't initialize the key fobs. I have tried to program the key fobs by all a different kind guides what I have found around the net...

Yesterday I replaced a GM5 module to our e46 (central locking problems) and there was no anykind problems to initialize the key fobs with the new module...

It's alive!!! I found the reason why my key fobs stopped working.
All of you who do not get the key fobs initialized, check the wiring near the right side hinge of the upper tailgate. There is a yellow/white striped wire that goes from the antenna amp to the GM5 module. The wire was broken inside the rubber boot in my X.

Rob if you need some help let me know I'm in Hawaii Kai.
PM me