I think either your battery is dead or you have a bad alternator. The battery light is lighting for one of two reasons. Either you have a problem with the charging system (which includes everything) or you have a problem with the associated sensor. What I would do is have my battery tested first to make sure it is in fact good. If that checks out then I would get the alternator tested. If it is bad I would go for a bigger one since you have to replace it anyway.
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