The starter won't engage. I turn the key to start, dashboard lights up normally, fuel pump energizes momentarily, but I don't even hear a click anywhere when I try to start it. Where do I start looking for the problem? The battery is brand new. The starter and everything else is original.

Edit: I made some headway in the diagnostics. I can start the car in Neutral, but not Park. This suggests a bad starter lockout/backup lamp switch. Where is that located?

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95 E320 Cabriolet, 169K