Looked on the web, where many sites indicated it was probably the starter relay. The hardest part was taking off the plastic cover so I could get to the relay! Once the cover was off, the relay was easy to take off. I shook and it made a noise -- another indication, according to the web, that the relay was bad. I looked up the part, found it online, and was happy when its pictures matched the starter relay I had. Ordered the part. When it arrived, it only took a few minutes to install it and plug in the fridge. No clicking, and I could tell the fridge was starting to work properly. Job done.