Can you describe them (like hail on a tin roof, like a firecracker, like sizzling bacon, like a duck when the lid of the breadbox accidentally closes on his beak...) What part of the car did they seem to be coming from?
Was there smoke involved? If so, where?
That's definitely Patrolman Ohm's way of telling electrons there's nothing here to see, move along.
First, remove the negative cable from the battery terminal. It ain't doin' you no good, and that way you'll *know* that any flakey circuits that are already known to emit a burning smell and then not work aren't going to be sporadically re-energized for random reasons.
When you safely raise the car and support it on jackstands, or maybe (with luck) you can tell enough from underhood, does the starter show signs of overheating (paint bubbled, charred wiring) or being mechanically busted, and is one of those things what smells? What about the big wires that you can trace back from the starter to wherever it is they go?
My old Thunderbird runs the power windows through a relay, but even slightly post McNamara-era Ford wasn't perverse enough to involve the starter in that, so perhaps your problems are higher up. What's going on in the big fuse/breaker box underhood and its small counterpart under dash? What about the other big wires in the vicinity of the battery and the alternator? What make, model, and year are we conjuring up in our minds?
BMW is not into the whole fusible link thing as much as other automakers are. I don't have a 328 manual here for anything newer than '86 but I think there is basically one fusible link in the whole thing, and it's on the starter.
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