Nice one about the McLaren: ask the real Hakkinen what he thought about his own McLaren Formula1 car lol. (I'm a huge Ferrari fan
Back to your question, I tend to agree with the dealer since the Limp Home Mode (LHM for short) can be caused but pretty much anything but since your car has been in Winter storage the first place to start is definitely the battery: a weak battery in a Mercedes can cause every kind of gremlins and weird behavior because all the electronic modules in our cars need solid power so before anything else check the battery and replace it if needed and see what happens. Now I suppose since you bought the car only a few months ago it probably has a few years old battery that is dieing.
Keep us updated.
Cheers.