You probably have already checked this, especially since it sounds like you already took out the battery. But have you checked to make sure that your battery connections don't need to be cleaned? The very first thing I do on any charging/battery problem is clean the terminals. Use hot water and baking soda. If you are in a parking lot somewhere, coca-cola from the nearby vending machine works too (that is why I don't drink that stuff). Make sure you use a wire brush (wear safety glasses) and clean botht the battery terminals and the cable connections themselves. There may be more to your problem, however it sounds like dirty connections to me and it is a good place to start. Dirty connections will do exactly what you are describing. It will start fine one minute and barely crank the next.

Good luck