Most likely the problem is the starter solenoid. I'm not familiar with your model, but I would expect the starter is very similar to the other Benz starters. These are very similar in configuration to the GM starter that has been plagued with "hot no start" problems for about 45 years.
If you can find a starter solenoid, replacing it will probably make your problems go away. If you can't, find a Bosch certified remanufactured starter and watch your problems go away for many years.
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in