I agree with Benzmac -- it's probably the fuel pump relay. I had an '84 190E that experienced the same symptoms you describe. I took it to the local MBZ dealer/shop; one test drive by the tech and he nailed it (as did you Benzmac) -- new relay (and $125.00 later) and I was on my way. Apparently the original relay is not hermetically sealed. Water vapor gets in them and corrodes the contacts/components. The replacement unit corrected this problem.
Hope this helps.
PS - the '84 had full AMG body, wheel, exhaust, and suspension package -- it was "sweet". Imagine how I felt when stalled at a light