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Replacement parts for KENMORE 10676239400 | AppliancePartsPros.com

Check your freezer temperature, it should be between 0 and 5 degrees F.

If the unit seems to be cycling correctly then it may be a thermostat problem.
Of perhaps the mechanism that opens/closes the damper which regulates the amount of cold air entering the fresh food section is no good.

If the compressor runs continuously.
Check that the evaporator fan is running. It is required to push cold air into the fresh food section and efficiently cool the air in the freezer.
Remove the cover inside the freezer so you can inspect the evaporator coils.
If they are heavily iced/frosted over you have a defrost problem.
If little or no frost on them you may have a sealed system problem.