Sorry I am not familiar with BMW's but Jaguar of the same era had a relay with a push button reset on top. When it failed (often after hitting a bump on the road, sometimes for no reason at all) the transmission would go into limp mode, you could not get the car out of park if you engaged park, and you had to start the car from the starter solenoid wire at the starter. The relay was on the left side of the dash on most XK8 and XJ models.
On your BMW this type of problem may be electrical wiring failure or anti theft issue. Sorry I can't be more helpful, hopefully one of the fellows here will see this post and know a common problem. Call a few BMW specialty shops and see if they have seen this problem before and perhaps could lead you to a blown fuse or be able to point out a common problem.