I had a problem in my old Benz a few years ago. It was hard starting at first. Then, as I drove at night, things slowly began to turn off. In order: radio, heating, interior lights then, eventually, head lights. The car still drove. By the time I reached the bottom of the driveway, the engine stalled out. My battery was fine, but it was my alternator that was the problem.
Its not exactly similar to yours, but perhaps applying a volt meter to your alternator (or starter) would better locate the issue. That's what I did. Good luck.