Product review (5 stars): Multiple Refrigerator Kit, Excellent Instructions, Parts Work Great!
It's hard to add more info beyond the very well written reviews already posted by J. Swingler, S. Tauchi and others. However, I'll try in the effort to create more hits for search engines to bring people here to buy these parts. The kit sold on Amazon is the same kit sold by appliance sites, but far cheaper. The kits are shipped VERY quickly, too (even without Amazon Prime).

As others have said, don't be mislead by the fact that the kit has lots of parts in it even though you only seem to have one bad part. The kit covers MANY different refrigerators. It is apparently based on the compressor used. Many refrigerator manufacturers use the same compressors.

Here are some of the brands that "may" use this relay kit: Whirlpool, Kenmore, Crosley, Estate, Kitchen Aid, Roper, Magic Chef, Maytag, Admiral, Amana. Contact your refrigerator manufacturer to find out what start device part number they recommend. Or, take off your start device (pictures and instructions can be found on many appliance forums) and look at the part number, then see below.

This kit sold by Amazon replaces the following "Start Relay" part numbers: 2188829, 2188830, 2188832, 2188833, 2188844, 2188845, 2188846, 2188847, 2212193, 2212194, 2216697, 2216722, 2220474, 2220475, 2220476, 2220477, 8201531, 8201532. There may be others, too. Check with your fridge manufacturer.

A bit of background on mine: It is a 2003 Kenmore Coldspot, part number 106.53659300. This refrigerator is made by Whirlpool (as are all Kenmore refrigerators starting with number 106). I have owned it since new and it always ran great. Then, in a one week time period, I had intermittent instances of ice cream melting, then getting hard again. One day, the ice cream melted and did not recover. A few hours later, the ice in the ice storage bin started to melt and my ice maker began spilling out water. The fridge seemed to be staying cold, at first, so I thought it was a problem with the defrost circuit. I looked at the bimetal defrost thermostat behind the metal panel inside the freezer, but that was fine. That's when I knew there was a bigger problem.

Thanks to the power of the internet, I found many helpful forums describing this problem. IMPORTANT: Several forums recommended that if your refrigerator is doing this, don't leave it plugged in. You might ruin the compressor or start a fire. Move your food to another fridge or several ice chests.

After I removed the bottom cardboard cover from the back, I found that the compressor was VERY hot to the touch. I unplugged the fridge for about 10 minutes to reset it, then plugged it in again. I heard a click, some quiet humming, then another click. The compressor never came on. The cooling fan was running, which was a plus. However, I've never seen so much pet hair build-up in my life! I have a dog and two cats and keep my house clean, but never thought about cleaning under the fridge. BIG mistake! There was literally zero air flow. I took off the lower front cover, too, then used a long wand on the vacuum to get the worst hair. However, to get it perfect, I had to use a small brush on a long handle and some compressed air, then vacuum again. It ended up looking like new.

I removed the parts from the left side of the compressor. In my case, they were only held on by a long, bendy metal clip. Just pop that clip off, unplug the wire harness, then pull the white/tan plastic box to the left away from the compressor. On my refigerator, there was also a square, black capacitor that came away with the assembly. This was a 5-minute job. Super easy!

The two-tone white and tan plastic box on my refrigerator is a combo start relay and overload device. It was TOAST! Literally. I'm kind of surprised there wasn't an electrical fire. It was charred black inside and stunk of burnt electrical bits. It rattled inside when I shook it. I decided to pry the halves apart. There was nothing left inside but little bits of charred debris.

Although the sealed black capacitor looked fine to me, several forum posts recommended replacing it at the same time. Since it is not in this kit, I ordered it seperately. Amazon has it for only $22. I figured that was cheap insurance.

All of the parts arrived very quickly! Then it only took 5-minutes to install them. One forum I read was posted by a single mom who didn't have the money for a repair. She chose to take a chance on this kit and was overjoyed at the low cost and the ease of installation. I have to agree. This easily saved me $150 in labor and it requires almost no mechanical experience. If you can operate a screwdrive and plug things in, you can do this repair. Just be careful to follow the instructions and compare the parts you have to the model number on the compressor. Another thing that's helpful is the color of the dot on the start device. The one that I took off had an orange dot. The one I put back on had an orange dot. That is what was required for my compressor.

End result, my compressor fired right up and all is well. Thanks to all who wrote good reviews and to Amazon marketplace vendors who sold the parts for a fair price and shipped them immediately.