OK. I just emptied the ice tray and there was water in the bottom of it. I felt the other freezer items and they are indeed thawing. The temperature in the refrigerated section seems to be warming up as well. I did adjust the temp settings last night to see if that would stop the noise (not sure why I thought that it might), so I just changed the temperature settings to coldest and I emptied the ice tray. I will see if the ice maker makes any ice and will see if the temperature cools down. This sounds like a compressor, right?
If the temperature does not cool off, can you tell me what a ballpark range might be on a repair like this (just a SWAG).