Just going by what you have said, I can pretty much guarantee the fusible link down by the starter is blown. Hence your alternator isn’t “putting out” jack that your car can use. Although many people never have an issue with it, the electrical system is half genius and half village idiot. That said, I’d bet if you ran a 6 gauge wire from the alternator to the distribution box lug you would be golden. I would probably disconnect the existing wire alternator wire just to be sure.