Not the person you're responding to, but as an appliance repair tech i can shed a bit of light. Many relays used on compressors will pretty much burn and disintegrate internally when they fail. When that happens, it will sound like a maraca--you can hear all the little bits and pieces shaking around inside. However, if you were to take a new relay and shook it, you'd hear a rattling sound. That sound is coming from the overload device. I've been fooled in the past, thinking the sound of the overload rattling was indicating a bad relay. That style of overload device rattles when it's at a safe temperature, perfectly normal. If the overload gets too hot, it makes an audible click sound. If you were to shake it then, you'd hear no noise coming from the overload (until it cools back down to a safe temperature, which varies between overload devices). Here's a pic of a common relay used on whirlpool refrigerators (which contains an overload device, shown in the pic beneath)

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I'll jump in before the lock, too. It's a shame it went that way, it's actually a good educational opportunity. If you can fix a pinball machine, you're probably capable of diagnosing and fixing problems with your appliances. Most of the time, the repairs really aren't difficult if you know what you're doing, or can at least follow instructions carefully.

Anyway, just wanted to say the problem OP has is simple: The compressor has 2 windings, similar to a 3-lug flipper coil--the compressor has 3 lugs as well. The relay/overload device attached to the side of the compressor feeds 120 ac volts to the low-resistance start winding (like the lower-resistance 'power' winding of the flipper coil). Once it's drawing enough current to get the compressor turning fast, the relay switches power to the higher-resistance 'run' winding, like an end-of-stroke switch on a flipper coil switches power to the 'hold' winding! Resistance measurements can be taken between the 3 lugs. Any open or very low resistance readings can indicate a bad winding, just like with a flipper coil.

So, OP's problem is most likely either the compressor is seized or it's got a broken/bad winding, or it's got a bad relay & doesn't switch the power from the start winding to the run winding on the compressor--not an uncommon problem. In any of those cases, the compressor typically hums as the relay activates the start winding for several seconds, but the relay does not switch to the run winding, producing lots of heat, and so the heat-sensitive overload clicks off to cut off power to compressor until it's cooled down. The overload is there to cut off power to the compressor if it won't turn over/run for any reason. Makes it safer, and may help salvage the compressor if the relay should fail (by preventing the start winding from burning up if the relay fails to switch the power over to the run winding).

As another poster above noted, the '3-in-1' hard-start kit can substitute many different PTC (Positive Temperature Coefficient) relays and is very useful as a diagnostic tool. It is a big capacitor/relay/overload device that can give some extra boost to the compressor to get it to turn over and run. Some also include extra wiring that attaches to the run capacitor *if* the compressor uses a run capacitor. I use them all the time on a variety of refrigerators new and old in order to determine if the relay is bad or the compressor is bad. Note it's only applicable as a replacement for PTC relays (which many are, but not all). That was probably more info than necessary, but what the hell. Maybe this will help someone someday?