I agree with everything posted above and think you should check everything suggested that you have not already taken care of.

That said, I think it's the starter. I just replaced mine and my '81 300CD has never started so well since I've owned it. I kept blaming batteries, compression, etc. , but it was a nearly worn out starter. The car would start relatively quickly most of the time, except at below zero. It would start then, but it took a little more coaxing. Now the car starts almost immediately at all temps. I love that.