Presuming it's not the starter going bad, I would check all the fuses first, especially fuse #5. Check the ground terminals in the engine compartment behind the right front strut for corrosion. If you can get under the car, check the wire in the lower engine wiring harness that connects to the starter.

Also, the neutral safety switch has been known to cause intermittent starting. Have you pulled the codes to see what's there?

There is a K38 relay behind the instrument cluster that you will find in this post. http://www.peachparts.com/shopforum/tech-help/269799-how-disable-alarm-1993-w124.html

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1993 400E, 256,000 miles (totaled)
1994 E420, 200,000+ miles
1995 E420, 201,000 miles