If your refrigerator isn't cooling, it could be the compressor. Turn the temperature knob all the way down then turn it back on. If you hear a fan but don't hear the compressor kick on, here's how to diagnose it. These instructions are courtesy of refrigerator repair houston.
First, buy a multimeter from the hardware store (around $20). A multimeter measures, voltage, current and resistance. Next, unplug the refrigerator. Remove the refrigerator from the wall and remove the back panel and you'll find the compressor. There will be 3 pins in the shape of a triangle. Test the bottom 2 pins and you should get a reading of around 10. Then, go from the top middle pin to the bottom left pin, which should give you a reading around of 6. Then, go from the top middle pin to the bottom right, which should give a reading around 4. If any of the readings are not even close, you have a bad compressor. If the readings all look good, then you probably have a bad relay overload, which should be a pretty cheap fix.