Subaru - Outback :: 2002 - Won't Start / Turn Over At All - Dash Lights Came On

I have a 2002 Subaru Outback Wagon. In May this year the OEM battery finally wore out, I was feeling poor so I bought a used battery from the local auto parts store. 2 months later, one day my car started chugging like it was having trouble starting and sounded like the battery was dying but then did start. Later that day it wouldn't start at all. Wouldn't turn over at all, but dash lights came on with key turn. Tried to jump it, wouldn't jump start. I bought a refurbed starter, had it put it, car starts.

A week later the same thing happened. Won't jump, no turn over, dash lights on when key turn. Had the battery tested, it was "good". Had the starter pulled, it was bad, put another refurbed starter in. Also replaced cables to the battery, and the clamp things that go on the cables to the battery. A week later, same thing, won't turn over, dash lights on with key turn. I was in the Costco parking lot when it happened this time, and got the tire mechanic to try to jump it. It jumped but was chugging like crazy and smoke came out of somewhere. The mechanic said he really thought it was a bad battery, that it sounded like the motor was trying to run off the alternator. I bought a new battery from Costco, and returned the used one to the parts store. When the used one was taken out, the mechanic said he could smell battery acid and it might have had a bad cell.

Now, the car will start when the engine is cold, but when I drive somewhere and it gets nice and hot (I live in Florida), it will not start again unless it is completely cold, or I get a jump. At least it will jump start now without a problem. I have had a mechanic use his little tool to check for computer codes, and of course there are none. I need to solve it not starting at all unless it is stone cold. My question is, what do you think is wrong?