To keep this simple, I will be using an example of a side-by-side refrigerator. Other styles will be different, but the principles are the same.
The first thing I go to, when checking a refrigerator or freezer, is the freezer(side).
Check the temperature in the freezer.
Listen for a fan running in the freezer.
Check temperature in fresh food
Go to the back of unit and see if the compressor running
See if the condenser fan, by the compressor, is running (if equiped).
( For the final 2 checks above, I usually can just hear compressor and the condenser fan, without having to move the fridge.)
If the answer to all the above is YES or GOOD, except the temperatures, then I visually check the evaperator coil, in the freezer. If it isn't frosting the whole coil within 30 minutes, you probably have a weak compressor or a "freon" leak. Neither one is usually worth fixing.
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