Forget the Bowdin cable-no way it's that I'd be willing to bet (with all due respect to Sr. FAD)...gotta be something that has to do with the kickdown switch.
Last year I checked out a 500E that my brother was looking to buy. Acted the same as you describe, Dave, and it turned out that the button part of the kickdown switch had simply come off, and was lodged behind the floor mat. I found it, popped it back in place, and the car was cured.
So cured, in fact, that the owner decided not to sell it!
You're in for some fun, Dave, once you solve this