When I shut the car off the Airbag light stays on, even when I take the key out and lock up the car. I dont know if this is coincidence or not, but the alarm is now going off after a couple of minutes setting it. And I dont know why the airbag light would stay on after shutting the car down (by the way , the airbag light goes OFF after starting the car)

So the alarm just goes off, for no reason at all, on a regular basis. I can shut it off, then after a few minutes it will go off. Even if I dont turn on the alarm, but just lock my doors with the key, it goes off. The only remedy is to leave the car with the doors unlocked, and the alarm off, not a good thing in NYC. As you can tell this is kind of an emergency...help !!

Any clues?

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2007 Corvette Convertible Torch Red
1996 MBz SL500
2008 Harley Davidson Night Rod Special