I wonder if you have a corrosion (or bad Ground) problem in the Positive/Negative Cables, or a corrosion between the Posts and Starter/Battery lugs (kinda common in Cars that sit)-I would try to see if I could isolate the Positive and Negative Cables by running a set of Jumper Cables from a known good Battery to the Starter lug (and Ground), and see if it starts-

What size of Battery Cables are you running?