If the battery has been used just for starting and the car hasn't been run around to recharge it, that could be the problem right there, especially if you haven't upgraded the alternator or the alternator pulley.
I'm not entirely convinced it's a charging system problem, either. How much gas is in the tank? How long was that gas in there? Did you use gas stabilizer? Try filling it up with fresh gas (don't have to use premium, just regular will do), plus some water remover, and see of that helps. Gas does go bad, hence they sell water remover & stabilizers. Good luck!
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Capri306, Moderator, The Mustang Works Online
1979 Mercury Capri, 5.0L -- C4 -- 2.73
1987 Mustang LX Notch 