Your model number is incomplete.
Kenmore numbers are usually 3 digits, a period and then an additional 8 digits.

Check to be sure that the compressor is running. You can usually hear it but also should be able to feel it vibrating.

is it running all the time other than when the unit goes into a defrost cycle or is it cycling?

If on all the time remove the cover in the freezer so you can inspect the evaporator coils.
If heavily iced/frosted over then it is probably a defrost problem.
if little or no frost then it is probably a sealed system problem.

Yes. If the compressor is running and there is no frost on the evaporator coils then it is a sealed system problem.

It can be repaired but it will be expensive and you will need a pro.
Often it makes more sense to put those dollars towards a new unit.

[COLOR="Blue"]It can't be the timer[/COLOR]
No. If the defrost timer was messed up the compressor would not run re:: stuck in a defrost cycle or the coils would be clogged solid with frost/ice re: no defrost cycles.

[COLOR="Blue"]or thermostat?[/COLOR]
No. The compressor is running so the thermostat knows that the ubnit is too warm and is keeping the compressor on trying to lower the temperature.

The sealed system is a closed look system. In other words there is nothing in the system that can control the cooling as long as the compressor runs the evaporator coils should get cold.

You are welcome

I just wish it was a better outcome.

Have been running around today shopping with the wife (great fun) and just noticed a typo "closed look system" should have been closed loop system. Hope this did not confuse you but it looks like you figured it out.