If the CTEK is showing green, leading me to believe that the battery is fine, it could be the immobiliser. I left my Audi sit for a while once and I had to hold the key next to spot in the car that then forced a handshake between the key and the car. Does the manual show any info in regards to what should be done if the key isn't recognised?
I googled BMW Z4 Owners Manual and found the below which is supposed to rectify if a connect to the key is lost and would assume the Plus Four manual should have something similar.
Switching the drive-ready state on via emergency detection of the vehicle key:
It is not possible to switch on the drive-ready state if the vehicle key has not been detected.
Proceed as follows in this case:
1.Hold the rear of the vehicle key against the marked area on the steering column. Pay attention to the display in the instrument cluster.
2.If the vehicle key is detected:Turn on drive-ready state within 10 seconds. If the vehicle key is not recognized, slightly change the position of the vehicle key and repeat the procedure.
Good luck
P
