Well, after some setbacks in ordering, I finally got the part late last week. This is the part I ordered (seems to be a good company):http://www.seneca-river-trading.com/ref-compressor-start-device-for-whirlpool-sears-8201799.html
Need to recap the situation before I give you the results. Recall that I found the electrical components that mount to the motor/compressor to be completely destroyed. It was as if they had been in terrible fire and came out as crumbly pieces.
Base on this, coupled with my intimate relationship with Mr. Murphy, my optimism was in the basement. It took me over an hour of filing the pins (in a confined area) just to get the melted metal off the pins. After that effort, my hopes were really in the toilet.
I got everything cleaned up and the parts installed on the pins and then plugged the fridge in. Nothing - I thought. Turns out the compressor had started quietly and was running like a Swiss watch. In a half hour the freezer was quite cold. I checked the connections quite frequently with the infrared temperature gun and they were fine.
So, it looks like it is fixed. For the near future, I will only run it when I am in the bus. That charred area really got my attention.
For the past couple of years, when the compressor would start, you could hear the inverter "grunt". When it started this time is was very smooth - no huge start load. My guess is that the start part was going bad for quiet some time.
Thanks for all the input that helped me avoid having throw that dead animal out the windshield.