Stop Lamp Switch
I'm not sure if it affects the idle or starting, but I know I had an ABS light and inoperative Cruise Control because of a bad stop lamp switch. This is a small module that sits behind the brake pedal. I think it's about $20, and takes around 10 minutes to replace.
Not sure if it's worth a shot - but I just replaced one on my 1995 E420 and it sured my car's ills.
Best of luck,
1995 E420 71k