[noahsdad]

Wow!
My '87 Deville just started doing the same thing. The fan runs all the time, even with the key off and pulled from the switch!
Here's the fix: The problem is in the fan motor control module, which is located atop the same housing where the fan resides, about in the center of the firewall. You'll recognize it by the two electrical connectors running to it, one with three or four wires, the other with two. There are four bolts which connect this module to the housing.
The problem results from an open circuit caused when the transistorized electronics fail inside this blower motor speed control. They sometimes fail because the blower motors are drawing too many amps, but unless you've had other problems, it's likely just the controller module.
If you can find one, get a replacement from a junkyard. The new ones (if your dealer still has one) are about $150. My local yard sold me one for $40 and guaranteed it for 30 days. It's a simple unplug, unbolt, remove - then reverse the process to install. Your blower should work fine after that.
However, these things fail frequently. You may have to do this again someday.
Good luck! Gotta love those Cads!