Battery would be my first guess, but you have that covered, unless it's a voltage regulator, bad alternator, or some other part of the battery/charging system. That could cause what you're seeing.
Outside of that, no clue. If you have access to a BMW diagnostic code reader that's probably going to set you on the right path. These cars have a lot of sensors/electronics, and trying to diagnose from the symptoms w/o codes is really difficult.
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