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It's the battery. It's always the battery. Charge the battery (on a real charger, not a trickle charger). Only after that is done would I move on to anything else.
I can kill the battery in my 79 by leaving the door open for a few hours here and there while replacing the carpet. Lights still work, starter does not. Charge for a few hours, good as new! I am more diligent about using the battery disconnect now.