I notice that my fridge was not very cold. I took a few things apart to troubleshoot. I found a little bit of ice build up where the cold air comes into the fridge from the freezer and that has been removed. It seems that the defrost fan is not operating correctly. It doesn't start on its own. I open the freezer door sometimes and notice that it is moving ever so slightly back and forth like it is trying to turn. If I flick the blade with something it will then start up and run until it needs to turn off. I assume that I need a new fan motor but I am not sure since it will run with coxing. I can tell the thermostat is trying to signal the fan because when I adjust the temperature adjustment it clicks and the fan starts wiggling slightly again. Does this sound like the fan motor needs replaced?

Thank you for your opinion, I have ordered a new fan motor.