It’s a pretty cut-and-dry diagnostic that the control is bad and needs to be replaced. There’s only about 2,000 different LG refrigerator control boards, and contrary to popular belief they don’t really go bad that often. They do — but in my opinion they have a pretty low failure rate.
With the number of boards they sell and the number they stock, they can take time to receive. Downtime = no fun. LG parts lookups are notorious for errors because of serial breaks, so they don’t always get the right control the first time. I’ve had this happen a lot with the Korean brands. You can only look up by model number, and the board is specific to the serial number. It’s very half-assed and causes a lot of problems, but that’s the way it is and there’s nothing I can do about it.
Example replacement board MSRP $623.53 (photo attached) — that doesn’t include the service call, labor, shipping, or tax.