If you turn on the wipers, the washer starts pumping water and neither the wipers or the pump will stop until you turn off the engine. You have to time it just right so that the wipers are in the down position or they will stay wherever they are when you turn the key off. i tried disconnecting the battery to re-set the computer, but that didn't work. Any ideas?

 

2006 wiper wont shut off

 

I had the same problem on a different vehicle, it was the wiper switch/high beam/turn signal controller on the steering column. The mechanic took all the covers from around the steering column and it was as simple as un-plugging the old one and plugging in the new one. I'm not saying your Cadillac switch is that simple to change but that would be the first thing I would eliminate