Conclusion: It needed a new battery. The good reviews here I can only confirm. The battery is 2/3 to load. Before first use, I still fully charged him. And then: Photos without end. After more than 100 images and mostly unfolded display (Live-View), a lot of zooming and focusing of the battery bar was still three bars.
The battery charger (purchased 2006), the battery easily accepted and fully charged. Could not be better.
Have already ordered me after the first experience a second battery. Now is an extensive photo session outdoors or on holiday no more obstacles.