E30 1987 325 Automatic Transmission

My automatic transmission seams to have gone out in a matter of a few days. First it started to stop shifting, then jerking / slipping. It drove ok for another day if I was very easy on the gas. Then it wouldn't even select a gear anymore. Do I need a new Transmission or is there another possible cause for this. Fluids are full, car gets regular service.
Can I determine exactly what unit I need by the VIN #1687327, or do I have to find out what flange I have by crawling under the car.