The fan is blowing in the refrigerator but the unit is not getting cold. I think the compressor is not working. How do I tell?

You first have to get an infrared ion detector from home depot. This will enable you to detect heat movements on the inside of the compressor dome while its functioning. Ultimately you can see the compressor function through a crude MRI. If they are out of stock ask sears or united refrigeration. The cost of the tool is relatively cheap compared to modern medical equipment. Its cost is around 1200 dollars but well worth the investment. You would want to do warranty work with out one. If your fridge costs more than the tool then just get a rubber mallet and give it a wack unless its not humming, in which case you should check the relay and overload and compressor windings. If its fed from a board make sure you have correct voltage to the csr.