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Replacement parts for WRT2154AW6 models | AppliancePartsPros.com

It does not sound like you have a defrost problem.
For defrost to be a problem the evaporator coils in the freezer must be iced/frosted over to the point where the evaporator fan cannot pull air through them to cool it properly.

I am guessing that the compressor is running all the time, other then when it is in a defrost cycle.
Please confirm this. You can usually hear the compressor running and you should be able to feel it vibrating and it should be warm.

If it is constantly running then it sounds like you are low on freon.
The symptom is frost only on part of the evaporator coil, usually where the freon enters the coil.
Take a look at the example pictures part way down on the following page
http://www.applianceaid.com/frig_notcold.html

It may be something else but low freon is the most common.
It will be a sealed system problem.

Check your warranty as the sealed system often has a longer warranty than the rest of the fridge. Be sure to read the fine print.

If you have no warranty then I have to agree with your husband as this will be an expensive repair and it usually makes more sense to put the dollars towards a new unit.