Replacing the Evaporate Motor fixed my problem. It was a very simple repair.
My problem was that the freezer was ice cold and freezing up, but the fridge was getting warm. Water was also dripping in the back of the fridge. The passageways between the freezer and the fridge were clogged with ice, which was melting and dripping into the fridge. Replacing this motor corrected the airflow, so everything is working correctly again.
The repair took less than 15 minutes. I did have to let the freezer defrost before I could remove the back panel on the inside of the freezer.