I was still able to get the car to lock/unlock with the key against the diversity antenna.
I remember a post were the diversity antenna was KO and the key was not working at all.

It is pretty easy to change, you have to open the tailgate and unclip the upper trim of the tailgate. 2x Torx bolt old the module and you just have to unplug it and plug the new one.

I was in the same boat, not sure if it was the key or the module so went to the wrecker and ask him if I could test the module he had on the carpark to be sure it was ok, took me 5min max to swap.

Just make sure the frequency are the same, mine was 315MHZ. The frequency is written on the module.

http://2009.bmwfans.info/parts/catal...nna_diversity/