Clicking sound after start relay replacement

I have an LG LFC23760 that is approximately 8 years old. About a month ago I started hearing a click, faint hum for 10 seconds, click. Then it would do nothing for 2 minutes and then repeat. Some days I didn’t hear the click at all. The fridge was still cool but in the last week it started to get warm.

I replaced the start relay and overload and the same behavior is witnessed.

Can someone tell me where/what to check next? The fan is running fine and the coils aren’t dusty or anything.

*** I should also state that while we were away on vacation for Christmas/New Years, we came home to a one giant single ice cube in the maker tray. We didn’t lose power so it if it is possible that something in the defrost components is causing the issue, we did appear to experience an extended defrost cycle (or failure to cool for whatever reason) but then recovered.

Update: New fridge ordered. Current is basically dead - only cooling that I can determine is coming from the blocks of dry ice I’m feeding it.

Still - I hope to identify the root cause and fix if it’s worth the money. Having gone through this issue - a backup cold box would be nice!