Wow, sounds identical to mine, except the abs light does not come on. From what I've been reading seems like yours may be related to the Overage relay. That's going to be one of the first things I replace.
Please keep this thread updated and let us know how everything works out for you.

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1986 560 SEC *Sold* < Big Mistake I miss my baby!
1988 300SE *Sold*
1989 300CE - current car, but not for too long