You are confusing, the state of the door being locked or not is not clear.
I read that you can use any of the electrical methods to lock and unlock the doors, but one of the doors remains with the button up (the status of the door being locked is not known). You can push the button (the black post that sticks up through the door panel) down, but it comes up again (and you do not mention the status of the actual door lock).
Because you are not clear, it sounds as if the door does not lock. You can use the car's electronics and the button does not move, and you can physically push the button down but it comes up again.
You are describing an issue with the Door Lock Actuator, Item 9 in this picture,
RealOEM.com - Online BMW Parts Catalog (You cannot use this picture because it's for an E36, so you have to find the applicable page for your car.) Alternatively, you can be having trouble with the (I think) the General Body Module. Somebody will correct me on this point...
To gain access to this item, you must remove the door card (the panel on the inside of the door). I think your car will have airbags in the doors, this means that you must not turn the key on to test your work else you will trigger an airbag fault that will require a trip to the diagnostic machine to clear. Disconnect your battery at the Negative (black) terminal while you are working.