[PxTx]

Don't rule out the battery having an internal short. You'll need a professional style battery charger (not one of those little guys).

If you can get something like 20 amps going into the battery and a separate volt meter at the battery and it reads 15v or greater, it likely is shorted internally.

These internal shorts can cause your alternator to full field when driving down the road aND bois off the good cells.