There are a couple things that need to happen for your refrigerator to get cold. The compressor has to run, the evaporator fan has to move the air around the refrigerator to cool down the entire inside of your fridge and freezer. There are a couple components on your refrigerator that are going to control when the compressor and the fan run. One being the defrost timer, the other being the thermostat or also called the cold control. I have made a couple videos explaining how to test each one of these parts and what they look like to help guide you along in your repair. I am still going to try to explain a basic walk through of what I would do if I was at your house.
The first thing I would check to make sure the Refrigerator was getting the proper voltage. If you open up the refrigerator and the light is on, we can move on. If you don't have a light inside the refrigerator, test the outlet that the fridge is plugged into and make sure that there is voltage at the plug in the neighborhood of 120VAC. Now that we have gone over that lets move on.
Thanks for taking the time to read this post and watch some videos. I hope that the information in here has helped you locate the problem with your refrigerator and you are able to fix it. If you have any questions or need some more help, I try to answer all my comments on my posts, either with a new post or in the comments themselves, so leave a comment with any questions you have or let me know if this helped you out. Make sure you thumbs up the videos and add them to your favorites, that helps me out alot.
Good Luck with your repair, I hope I was able to save you some money by you not having to call out a professional.