So, if it works all the time when you apply power directly to the starter harness, then I would suspect the starter is okay and the problem is somewhere between the positive battery terminal in the trunk and the junction box up front. All I can think of would be the ignition switch or the anti-theft device.

I did replace an ignition switch on my old 400E about 16 years ago. If I recall correctly, it wasn't that difficult, but it also wasn't necessary--I just ordered the ignition and tumbler all in one order.

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