Jim, do you know what the code is that is turning on the check engine light? It might not have anything at all to do with the transmission. I'll be glad to scan it if you want to bring it over sometime. You can also get the code by turning the ignition on-off-on-off-on, and counting the blinks of the CE light. Then call me or google the code.

What does this lady look like? Would it be worth a drive to Riverdale to check her out...oops, I mean check out her car, LOL. ONLY KIDDING.
From your description I'm assuming that the BMW engine doesn't turn over when you try to start it. First I would have her turn on the headlights and watch them while she attempts to start it. If the lights come on bright but go completely off when she tries to start it it's probably just a dirty battery post. If lights stay on listen to the relay while she attempts to start it and see if you can hear it pick. You can usually hear a starter relay close. If it is picking you might jump the contacts and see if that makes it turn over. If it does the relay is most likely bad. If there is power to one side of the relay and jumping it doesn't make it turn over then the starter is probably the problem. I'm not familiar with a 75 BMW so there could be some other wiring connections in the circuit that could also cause the problem. I did have an 83 BMW 328I and I do know from that experience that the best thing to do with a BMW is to sell it.