A refrigerator that makes a buzzing or humming sound and doesn’t keep the food cold may have a blown compressor (big bucks) or just a bad overload or compressor relay (about $20).
I had this exact problem with a refrigerator and called Costas Stavrou, our appliance consultant. To avoid n expensive service call, Costas suggested I first try unplugging the refrigerator for about 20 minutes to allow enough time for the compressor to cool and any on-board computers to reset. When I plugged it back in, the problem returned. So he suggested I buy both an overload and a compressor relay (or a universal relay kit) from the appliance parts store and install it (see photo). If the problem went away, it would be a $20 fix. Unfortunately, my compressor noise returned (meaning it was toast). I had to buy a new refrigerator, but at least I didn’t have to waste money on a service call. Instead I applied that money toward a new fridge.