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Parts for Frigidaire FRS6R4EWC Refrigerator - AppliancePartsPros.com
First confirm that the compressor is running all the time other than when the unit goes through a defrost cycle.
You can usually hear it but also should be able to feel it vibrating.
Is the fan you say is running the evaporator/freezer fan or the condenser/compressor fan?
Confirm that the evaporator fan is running.
If it is running all the time, remove the cover in the freezer so you can inspect the evaporator coils.
If they are heavily iced/frosted over you have a defrost problem.
If there is no frost or frost in just one area (usually where the freon enters the coils) then you have a sealed system problem and it will be an expensive repair.