Q: Alternator, Serpentine belt, or battery?

So, my car had died about a month ago after having about a week or so of really soft starts. I got it jumped, I unhooked the positive from the battery and it ended up staying on. The internet told me this means it's not the alternator. So I buy a new battery from Autozone and the car starts working normally again.

Now 2 days ago, so a month from my purchase of the last battery, I was driving home and the engine shut off while at a stop light. It wouldn't turn back, it wouldn't even crank. I got it into neutral and pushed it to the side and got towed home.

We tested a few things, if it would turn at all (it didn't) and if anything in the car worked (it didn't). Not even the electric windows would roll up.

So (yesterday) we jumped it, left it on for about 30 seconds and it died. We bought a new battery and it started but i unhooked the positive battery cable and it died instantly.

Is it just a bunk battery or alternator issues and could it possible be the serpentine belt?
My car has an automatic transmission.