I wouldn't waste time with the current battery, it sounds like it is on its way out. Swap it for a known good one, or buy a new one. Then, as mentioned above, do a systematic check of everything, BEFORE you fire it up. If it has points, file them a re-set them. Check the fuel filter. Sitting is the absolute worst thing for old cars, that's why I start mine every couple of months, regardless. And I live in the snow belt, so it isn't easy, it is bloody cold in my storage building! Good luck, I hope it is just your battery!