internal short, water getting inside it, someone stabbing it with a screw driver, cable loose/broken/frayed/not doing what its supposed to be doing.
more info, what were you doing when it stopped working? are you sure the cable isnt just loose? are you sure the cable that "tells it to charge" is making a connection?
i dont know whether yours is a genuine jap ae86, but we had an issue in my mates ke70 (same shit) where we didnt connect the wire to the alternator properly, not the big thick on, the one that tells it to switch on, so nothing worked.
if yours is a home-made (not saying its not quality!) job, it'd be worth a look...?
Eldar.O.
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