Places to start:

Check fuses.

Check voltage on battery with meter if possible. Healthy battery reads about 14.5 volts when engine running.

Through personal experience I have found that low voltage, either through sick alternator or dying battery creates bizarre electrical behavior well beyond the old dimming lights symptom. Just before it gets really ugly, all the warning lights in the cluster will go beserk, and the radio acts really weird, if I recall correctly.

What's the condition of your engine wiring harnesses? one of wires (or more) may be grounding out?

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1995 MB E320 Wagon
2001 BMW 530i
2007 MINI Cooper S (!)