Most refrigerators have a limited warranty on the sealed system. Kenmore Elite is 10 years. You should first contact the manufacturer of the refrigerator to check your warranty.
Most compressor jobs cost between $800–$1200 depending on the cost of parts.
In the US you MUST be registered with your state and hold an EPA certificate to enter a sealed system. Unless you are qualified, certified and registered, you should not attemp to do the repairs yourself
Refrigerators and vehicles have different systems and are not repaired the same.