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I have a 2000 dodge startus 2.5L and blower motor would still stay on with car turn off and no key in the ignition. Ireplaced the ignition switch to resolve the issue.
Mine blows air regardless, although it's just the natural airflow (which I usually just redirect to my feet since I can't feel it there..) Is this what you're talking about? Or is it the actual blower is on and running? I would try what craveyj suggested, and also try cycling the blower switch a few times. The switch may have just gone though.. (Did you try to turn it off and then it stayed on? or did it just start one day even though the switch was off initially?)