My Kenmore refrigerator model # 253.7419240p the

the fact that the freezer is still cold is a good thing as that means the compressor is still running, and probably at least the condensor fan also that is beneath the frig/freezer near the compressor.
check that the fan in the rear of the freezer is running when the compressor is on, if so then your issue may be a pluged or blocked air passageway that interconnects the freezer compartment with the frig to cool it. this will need to be chased down and located to remedy
if the fan is not running you will need to find out if there is power to the fan, if so the fan is shot and can be replaced, if not then we need to find out why. broken wire between the defrost timer is a possibility, even a bad connection through a moly plug could cause it.
hope this helps,
best of luck,
ttfn