Just bought a 2003 e320, having issues starting.
Also, if the battery was completely dead just letting the car idle won't charge it sufficiently. It'd take a good 30 minute drive or so to get it charged back up, or use your battery charger directly connected to the battery.
You can read your battery voltage on the center cluster display by following the instructions in this video, Basically, engine off and key in position 1, and with the center display set to the speedometer press the reset button three times.
The battery voltage should be above 12v with the engine off, and somewhere around 14 with the engine running. Keeping an eye on the battery voltage while cranking and with the engine running will give you an idea of where the problem might be. If the voltage drops significantly during cranking, suspect a battery problem. If the voltage doesn't go up to 13.5-14.5 while driving, start by checking out the alternator. A really bad battery could cause the voltage to read low even if the alternator is working properly, though.
When you say "it wouldn't start" did it crank and not start or no crank at all? If it cranks you likely have a bad crank sensor.






