The first thing I would do is make sure that it has the correct ignition switch installed. Starting in model year 2002, the S-Class used the EIS, as well as the instrument cluster to store the vehicle mileage. It's what's known as "Redundant Distance Storage". It's possible that the EIS was replaced prior to you buying the car. If the wrong one was installed there will be a conflict between the ICM and EIS. I've seen this happen on a couple of occasions. It's also possible that the EIS or ICM has simply failed, although I've never seen a faulty EIS or ICM cause the problem you're having.