[richappy]

If your compressor fails to start, you may just need a new start device.If your compressor hums, then clicks off repeatedly, unplug it to avoid compressor hard start failure! Warning, if the lights dim, or the compressor hum is really loud, you may have a shorted compressor winding, or a grounded winding! Just check with a meter.
If ok, verify your compressor is getting 115 volts.Check with the compressor plugged in to avoid false readings.
If ok, next measure the inrush starting current with an amprobe. If 15 amp or less(assuming the compressor horsepower is less than 1/3, most are), then you may be able to fix it with a new start device. Just order the factory replacement device and NOT a substitute and install it by removing the compressor side cover and prying off the device.If the overload klixon and start relay are separate items, just remove and replace both. Just make sure the run capacitor (if your fridge has one) is wired between the run and start compressor pins, no change to the refrigerator wiring will ensure this, just verify. Normal run current now should be less than 2 amps. If the compressor now fails after a short period of running, it has seized up due to varnish buildup or a burnt winding. and may not be repairable.They do sell a compressor additive, Supco 88 that will dissolve varnish, but it must be installed by a pro.
If the compressor fails to start with the new device and the compressor is less than say 8 years old, your compressor is NOT fixable,your start/run windings are burnt or the compressor has seized possibly due to varnish buildup.
The use of a universal 3n1 hard start kit for this failure is NOT recommended, the newer compressor start winding will burn out from the high inrush current and if your fridge has an adaptive defrost board the high inrush current will blow out the relay or triac real fast.
A lot of the older refrigerators like the old GE's with the hot dog shaped compressors can safely function with a 3n1 hard start kit, so for these it's safe to use, just check the name plate for total current draw, if above say 2.5 amp it's ok.
If you want to use a universal start device like the URO41 be aware this device will not thermally protect the compressor and will allow higher power surge inrush current than the original klixon.It comes with run capacitor wires and you will need to properly identify which compressor terminals are common, start and run to properly connect it.
The PRIME compressor burnout protection is the original klixon overload device, a thin device attached to the common compressor terminal. If this is ok, you can retain this, and just replace the start relay with a IC1 ,a universal semiconductor start device. This will give good compressor protection, but it has no provision for wiring in the run capacitor. Just be SURE you wire in the original run capacitor if the fridge. has one,failure to do so will ensure compressor failure. This capacitor is always located near the compressor.
Also, when checking the compressor terminals, the start winding, has the higher resistance when measured from the common pin, the run winding, less resistance.The common pin is usually on top where the original klixon unit was.
One word of caution, if you use a non-factory authorized start device, it will void your compressor warranty. If I use one, I tell the customer about lack of thermal protection (usually not a problem) and explain the correct part should be installed, usually the customer waives that extra expense.