How do you know if batteries are dead in key fob as car clicks but wont start on 2000 Mercedes-Benz S430

The car has a new automobile battery from MB and it was tested and shows full charge. Lights and electronics come on, but car clicks and will not start. The first time battery was installed the car ran fine. The second time I went to start it will not start.

Asked by for the 2000 Mercedes-Benz S430