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So it's hard to know exactly what's wrong, but you'll want to pull the refrigerator out and remove the lower back panel to see the compressor. Touch the compressor and if it's really hot, then maybe unplug the unit for 24 hours to let the unit cool down and try again. If it still doesn't cool, then the compressor has gone bad due to the poor ventilation as you suspected. If the compressor isn't warm at all, then you likely have a bad thermostat not telling the compressor to turn on.
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