Diagnosis
This sounds like the damper door isn't opening. Cold air from the freezer flows through a duct into the fridge section, controlled by a damper. If it's stuck shut, the fridge warms up and the compressor runs non-stop trying to cool it.
How to Fix It
The damper assembly is located in the back of the fresh food compartment, up top. You'll need to remove the plastic cover. Unplug the fridge first. Once you have access, you'll see the damper door. Manually see if you can slide it open and closed. If it's stuck, check for ice or an obstruction. Often, the motor that moves it fails. Listen for a faint whirring or clicking when you change the fridge temperature settings – if you hear nothing, the damper motor is likely dead and needs replacing.
If That Didn't Work
If the damper seems to be moving fine, you might have a separate issue with the main control board sending the wrong signal, but that's rarer.
Heads Up
Before you order parts, do a quick test. Set the fridge control to its coldest setting and listen carefully right at the damper cover for about a minute. If you don't hear a small motor trying to actuate, that confirms the motor failure.