Alrighty, I need a little help

I have a 94 Mustang GT Convertible, heres the problem.

At first, after starting it might sputter and die, or it might not...it depended on its mood. If I gave it gas it was fine, and if it felt happy that day it was also fine. The battery light would also come on while the car was running if the window switch was pressed, at times, this is with no other power draw for accesories.

Alrighty, so I decided to change the negative battery terminal because it was very corroded and the bolt was rather stuck so I couldn't remove the terminal if I wanted to. This had nothing to do with solving the previous problem, but it may have something to do with the new problem. The new terminal is not the same as the old terminal, I can take pics if needed, but it fits fine.

More recently, I was sitting at the airport listening to music with the car off. I went to turn the car on and it simply wouldn't turn over, acted like itwas going to but it was like the battery was dead. I checked the new terminal, noticed the ground cable was a little loose, tightened it back up and tried starting it again...for the same result. Finally I held the key on start for close to a minute and a half and the car started. Drove it home and no more problems for about a week.

Now it starts like that again, all slow and like the battery is dying. The battery light comes on when I mess with the window switch, and....the gas gauge reads absoloutely empty on startup and for most of the first trip of the day even when the gas tank is full.

So what is the problem, and how do I fix it?

THANKS GUYS and GALS
 
If the batter light came on , I would take the battery to get tested, maybe an alternator issue, the car not starting also kinda sounds something up with the starter, but I could be off, I would chk the battery at a parts store, clean terminals on the starter, and most parts store can also check the alternator.
 
yep - parts store check up sounds good.

absent a component failure, I would go over the motor grounds - they are around the oil filter on the block. If you dont have proper ground (juice flows from ground to positive), a nuclear powerplant wont start the car.

I have used a jumper cable as an auxillary temporary ground (when it wont start) run a jumper cable from the neg battery cable to good clean metal on the motor. If it starts, you have an insufficient power ground.

good luck.