Sounds like a similar problem with my freezer bottom refrigerator. The auto defrost cycle was not working to keep the ice dam from forming. Once the back vents are frozen over, no cold air gets to the refrigerator unit on top. My problem was a bad evaporator heater thermostat unit. A low cost and easy item to replaced. My unit was clip to the evaporator coil. Cut the wires and re-splice in the replacement to get it working again.
Cool head, July 2009