I highly doubt it's something as simple as a fuse, we are talking about a BMW after all...lol!! Sounds like it may be your GM (General Module), it's a white electronics box located behind glove box, you have to remove the glove box. It looks like a white video cassette tape, again just like the key cylinder it's an oh so common failure item. It controls the dome lights, wiper, central locking and of course the remote lock and unlocking. It's amazing how something with no moving parts inside can fail so often. so now you have an idea of what's in store for you down the road...lol! Welcome to the world of German engineering at it's finest...lol
! Do a search for GM module and you will find a thread about how to find and remove it, it's really simple. Then you can send it to this guy to have it repaired, he can also repair your key if it's broken also. Yes the remote keys fail quite often also, so you could have bad key also, he repaired mine and then I went to the dealer and bought a new one, now I have two working keys, click on the link below.
BMW General Module 5 (GMV, ZKE V)