Yesterday my electrical system shut off completely - it was a loose cable on the battery. It was tightened and fine. Today I pulled out of driveway and check engine light on -- are they related to battery? Other?

Does it have spark at the spark plug's ,fuel pressure , compression . Do you know how to test for these ?

We suspect an intermittent electrical connection that drops voltage to the fuel pump. Likely at a point where the major electrical wiring harness cables plug together under the hood near the battery. Open the connections and inspect the joints that look like an overheated joint like the plastic carrier plug showing heat stress around the plug connections.

Open hood and look at left side of engine compartment. Find the braid jumper going from engine block to fender. Grab hold and wiggle. It may be loose from corrosion at the fender end. If possible tighten. If not replace with a new heavy jumper from block to body of car. This a major design flaw since battery charging current and starter current is forced through this skimpy wire and connection. I replaced battery and alternator twice before discovering this defect.

My first thought would be the horn relay is sticking.
Or a short in the horn pad on the steering wheel.

Check fusable links

it might be the solinoid on your starter motor, try tapping it with a hammer (its ok it is safe to do so) as the ignition is turned at the same time, it might free it...just an idea

maybe the fraying belt knocked your wiring or plug loose check that

Well, it sounds like the loose cable goes back into the transmission -- that would be your speedometer cable.

This cable would not cause electrical problems, but something pulled it from the transmission and may have, at the same time, pulled an electrical wire loose. I would check the transmission and surrounding area for loose wires.

chad you need to check yhe fuses. theres a fuse for alt. if its good then yes alt is probably bad

Sounds to me like a poor battery cable connection. I am not familiar with the BMW cable routing but it should be simple enough to follow and repair.

First disconnect the negative cable from the battery and leave it disconnected until the final step.

Dicsonnect the positive battery terminal, clean the battery and cable terminal with a wire brush or light sand paper. Apply some dieletric grease or light coat of chasis grease and reconnect the cable to the battery. Follow the positive cable and do the same procedure to all connections down to the starter. Along this route you may notice a smaller wire connected enroute with a fusable link or fuse. Make sure to check these for loosness and or melted wire coating this can be a sign of a loose connection and your problem.

With the positive cable connections completed and reinstalled. Do the same to the negative cable, remembering not to reconnect the negative terminal to the battery until the very last step.

Sorry I don't have more knowledge of the wiring on the BMW.

Hope that helped.
Good Luck