It could be many things but you are describing clasic dead battery syndrome. It may just need a good charge (with charger, driving around may not be enough) or it could be a goner.
Read this, http://www.mbusa.com/care/client-care/roadside-assistance.do
If I remember correctly, they can also install a new battery, no labor or delivery charges, you just pay for the battery.
Good Luck, Dan

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2012 E350 Bluetech