Gilly, tabo, thank you!

You're right, Gilly. The problem has got to be electrical in nature.

I failed to mention that the auto-dimmer feature of the rear view mirror also fails to work when this phenomenon happens. The little green light doesn't come on.

That makes 3 unrelated malfunctions caused by a bad ignition switch most probably?

As soon as I crank the ignition to position 2, and see that neither the trip computer, Airbag dash check light, and auto dimmer for the rear view mirror come on, I know they won't come on when I fire up the ML's engine.

And yet, the next morning I start the ML, they all light up as if nothing had happened.

This happens 50% of the time. Weird.....

Before I bring out the sledgehammer, I'll try observing and checking the connections first (under the fusebox, maybe) then have the ignition switch checked.

Cheers, gentlemen!