Listen for it, if you heard it once and the compressor is not so hot on the top that you can hold your hand on it that is the problem. The compressor is only running sometimes. The reason to check for the heat is to be sure its not burning up inside. If you can hold your hand on it than it is not. Its a very good, reliable way to test.
The part mounts on the side of the compressor and is held on by a retainer clip and cover.
To replace that part UNPLUG THE UNIT. Remove the retainer clip and cover and pull the part straight off. Have the new part in hand and remove the wires one at a time and place that wire on the new part one at a time so the wires do not get mixed up.
The best thing to do is take the parts in hand to an appliance
parts store and let them match up the part because I do not believe that number listed on the parts list is an exact replacement part. I think that is going to be a generic number even though it is the one Frigidaire has listed as the replacements I stated above this is probably going to be the problem it is a very common failure, and it is going to be the only thing you can do to attempt a repair. There is a very very small chance the compressor is bad and if the repair does not work you will have to call for service. If you do the following is what you need to know before accepting an agreement for service.Do you have a license to recover freon?
(They must be licensed its federal law) That way they just cannot come out without you knowing and charge you then leave because they do not have one. What is the minimum you charge for a sealed system repair?
Please ask me if you have any questions at all Roman. If not please leave a rating for me.