The problem you describe exibits all the symptoms of a bad battery pack. The thing that throws it off is that it only happens when the engine is running. But if it's only charging about halfway and your charger thinks something's wrong with the battery, I would try a different battery pack. I bet that would solve the problem. You pack may have a bad cell or a bad connection within the pack. That's the only thing I can think of that would cause it to act funny only when the engine is running.