i'm not an expert but i just replaced my door lock actuator last week and i got to know that area fairly well. i'll try and make some guesses and solutions.
the key goes into a brass mechanism which has a finger sticking out in back. that finger goes into the door lock actuator.
my *guess* is that, since this piece was probably not designed to withstand daily use, this is what broke. i'm deducing this from your description of what happened. if it is, the replacement is super easy, but that's another story.
the problem for you now is how to get into the car because once you do, my guess is that you *should* be able to open the door from the inside handle.
i don't know how to break into the car other than to smash a window. this car is sealed up pretty tight. my X5 got broken into one night. they just pried the cylinder. if you just stick a big screwdriver into it, it is easily destroyed. but this is not your solution because if that finger is broken, then you would need to get the lock cylinder out and all the stuff behind it as well including the broken "finger." then you would eventually get access to the slot in the door lock actuator. stick a screwdriver in it and turn. the door would get unlocked.
have you asked BMW for help?