ccb,

I don't think it's the starter. It might be the starter switch but not the starter. The real problem appears to be your battery and cables. There is something going on their that isn't right.

All cable connections must be tight, clean and sound. Cables should have factory ends on them. Replacement, bolt on ends are bad news. To clean the positive post and cable, you need to actually scrape the coating off with a knife. When you see bright new lead you're in business.

Take a look inside the little starter switch on top of the starter. It's pretty simple and it might be the source of your problems. Good luck.

Stuart