Old unknown Hotpoint fridge compressor problems. Single phase motor and relay help w/pics

I bought this old Hotpoint refrigerator as a project fridge.

I turned it into this airtight temperature regulated beer fermentation chamber.
I do not know about refrigerators, only how to build.

This is the setup.
-I have the fridge plugged into a temperature regulation device (grey box sitting on chamber extension) that provides it with power when necessary.
-I also have an interior heat source plugged in to the same device.
-This device allows me to set any given temperature I want the chamber to be.
-I choose 70° for beer fermentation reasons.
-The device grants the refrigerator power to cool when it needs it to. Once the temperature drops below 69° it kills the power to the fridge, turning it off.
-It then turns on the power to the heat source until it warms back up to 70°, then it kills the power to the heat source.
-The fridge sits stagnant until the interior chamber naturally warms to 71° and then the temperature regulator kicks power back to the fridge, turning it back on to cool.
-The process repeats over and over again.

So, I came back to the fridge at one point and noticed that it was off, and the interior temperature was at 80°. I unplugged it from my regulator and then directly into the wall and nothing. The light was still on inside so I know that the fridge was receiving power but the compressor wasn't starting up. Did I overload it? Did I kill the relay? Did the compressor give out on me? Something tells me that I put too much stress on this old girl with the frequent off/on sequence that it has to go through to maintain a consistent temperature.

After some thorough research, I read that the first thing I should test is the compressor relay; so I read faqs, forums, and watched tutorials on how to safely remove the piece. I learned that this style fridge had a single phase motor with an old current relay.

Once I carefully removed the hinge that holds the relay tight against the compressor...I attempted to pull it off, but it crumbled in my hand. It was extremely worn and fragile and ready to break without any sort of pressure.

Here is what I have remaining of it:


Am I right? Is this a "current relay" to a single phase motor? Does this differentiate from a "starter relay" on newer fridge's? I believe that the motor is also in the pic... please correct me if I am wrong...
What do I do? Is this relay replaceable? Would the motor need replacing as well? I'm pretty sure that these model motors/relays were discontinued, but I found a similar model online. You can see that here:
http://www.geindustrial.com/publibra...3ARR18|generic

Is this the same thing? Will it work if replaced with this part?

They are not the SAME exact model but are very similar. Most of them say that they are for washers/dishwashers. I do not know if they would work for a fridge.

I would be extremely grateful for any help or advice. I apologize for my lack of knowledge in the situation. I am pretty handy so I am hoping to be able to repair the fridge. I'm just really hoping that my compressor didn't blow, leaving me with the only option of replacing the fridge. You can see that the chamber has be customized and measured specifically to this fridge's dimensions. Replacing the fridge (the cooling source in this project) would require much time, money, labor to say the least. I'm trying my hardest to avoid that.

And last but not least (and as an absolute last resort); if I was to replace the cooling source for my chamber would something else other than a full size refrigerator be better to use? Any recommendations?

Thanks for any help that may be given.

-BCB

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