Have you checked all the fuses? I think there are 3 fuses for the central locking system, I had the same issue as you and resolved it by replacing 1 blown fuseCan lock the car all doors and boot ( 1.9 preface lift 1999 Z3) with the key. But not from the fob remotely. How can I check the RX in the mirror. I only have one key. Cant really find anything in the post to help.
Sounds complicated to check the RX in the mirror.
I feel your pain mate, I am to this type of Tek what Bryl Cream is to Kojak.Think I am going to have to bite the bullet and order the bits for to look at the signals. Sound like a job for my lad who is into modern computers. I am an old fashioned computer engineer whose expertise stopped in 1991 with the Ferranti Argus 700 used to fly the Bloodhound S.A.M.

old fashioned computer engineer