I have a 10-year old upright side-by-side Kenmore fridge/freezer (253.52649304). Has worked great until last night.
Last night, I noticed a low hum seeming to come from the freezer side. Everything else seemed fine. This morning, the freezer was noticeably warmer but the fridge seemed fine.
By supper time, the freezer was at room temperature and the fridge had gotten noticeably warmer as well.
Both temperature dials are at the recommended dial setting.
Remove the rear cover so you can access the compressor.
It should be warm (not hot) and you should be able to feel it vibrating.
Be careful when checking it, in case it is very hot.
Is the condenser/compressor fan running.
If the compressor is OK then remove the cover inside the freezer side so you can inspect the evaporator coils.
Is the evaporator fan running?
If there is no frost on the coils then you have a sealed system problem.
If there is just frost in one area (usually where the freon enters the coils), it is also a sealed system problem. Likely low freon.
Be sure that the compressor has run for a couple hours, if you do this check shortly after a defrost cycle you could come to the wrong conclusion.
If it is a sealed system problem then it will be an expensive repair as you need a pro.
Often it makes more sense to put those dollars towards a new unit.