E46 Wipers still going when ignition off

Two days ago I drove home in the rain with the wipers in the intermittent mode, and I left the switch in that position when I turned off the ignition. Today is the first time I used the car since then. As
I approached the car, the wipers swept one sweep across the windshield. About 15 seconds later, they did it again. When I started the car, the washer fluid indicator stayed lit, and I get several warning chimes, although the washer fluid tank looks full. At the same time that this happened, neight master key's remote will lock or unlock the doors. I haven't had my the car very long, but I didn't see anything in the manual about any button I could have accidently pressed or anything. I do not have the rain sensing wipers (at least I don't think I do).
I would have thought that the battery would be run down if the wipers ran for two days, but the car started right up. The doors lock and unlock properly by turning the key, and the wipers and washer appear to work normally, but the washer fluid light is still on.
Any help?
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David wrote:

This is not normal. Is the car under warranty?
JRE
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It is a 2001, so it is out of factory warranty. I have an extended warranty, but not from BMW. Since my original post, now that it is dark I have discovered that the dashboard lights for the odometer and the headlight switch are staying on even while the ignition is off. Could it be that the car "thinks" I am still sitting in it, so the remote locks don't work and the lights and wipers keep working?
However, the warning chime was apparently the seat belt warning, which I never heard before because under normal circumstaces I usually fasten it before starting the car.
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David wrote:

Sounds like a stuck relay. You might want to give them a tap one-by-one.
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Thanks, Jim. Any idea where the relays would be located?
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David wrote:

There is a 16 minute period after you turn the ignition off where these lights (and if automatic - the shifter illumination) will stay on. Wait 20 minutes and see if it is still on.
I missed the part about the remote locks - what is the problem there?
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admin wrote:

Problem was diagnosed by dealer as faulty instrument cluster. When the instrument cluster remained powered, the central locking is disabled. Replacing the instrument cluster restored everything to normal.
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