Blower just runs on its own even when the key is out?

Should I be looking for a new blower motor or does this sound like a short of some kind when blower just runs on its own even when the key is out?

A few weeks ago my wife's car wouldn't start. I tried to crank it and the blower turned on by itself, but the car was not starting. I jumped the car, and the blower just ran. I couldn't turn it off. I switched b/t hot, cold, and defrost and it just ran.

I turned the car off after about 10 minutes of letting it run and the blower was still going. The next morning the battery was dead, so I figured the blower running killed the battery. I jumped it again and this time the motor didn't run at all no matter what I did. I wiggled and checked fuses and wasn't sure which controlled it but it still didn't turn on. She drove it for about a week and then one day it wouldn't start again.

When I put the key in and tried to start it, the blower turned on again, so I figured it turned on sometime during the night and drained the battery again. I have not jumped it again since then. I think the blower is working, but maybe a short or something is causing it to run on its own.