1985 Pontiac Fiero Battery Drain Problem

I tested all of the fuses and non of them seemed to trigger anything suspicious. I thought maybe that the terminal posts that I replaced on the battery may have solved the problem so I charged the battery with a battery charger and it started up. I drove it down the street and back and turned it off. I waited a few minutes and attempted to start it again and it was already dead. It seems that the battery is draining on the car itself and not recharging. And after talking to my dad he actually did NOT get the alternator tested due to the fact that on fieros you basically have to take the entire engine out to get to the alternator. I will test it using the methods posted on this website. One other thing though. The negative battery cable ground wire is rusted out and dosent look like its in good condition, is it possible the battery drain could be linked to that?