Thanks Doug regarding the 15K label. I just visited an old Dometic page and found the Penguin described with 11K, 13.5K and 15K units. However the updated Penguin II shows 11K, 13.5K and High Capacity units. So thanks for the clarification.
I took another dozen trips up top the RV to look and test some more. The solenoid coil does work as I pulled it off and it attracted a screwdriver when I connected and disconnected it. I do not have an ammeter that will test beyond 10 amps but I did connect and disconnect one of the compressor leads and got some arcing (nothing serious, just a quick little flash). I could also hear it stop and start up again, so that was working.
But while I was up there I noticed a spot on the compressor that was a little darker in color. Looking more closely I found that some small diameter copper tubing (about an eight inch in diameter) next to the compressor had rubbed through and created a hole in the tubing. So my refrigerant has leaked out and the cause of my problem. After a few calls around it was determined that finding someone to fix the leak and be able to recharge the sealed system as on RV units was like finding hens teeth so back to ordering a new unit. Why do they not provide ports to recharge these system?
Still going with the High Capacity Penguin II but only doing one rather than both units since the other one is (knocking on wood) still working for now. So we will be buying the downgrade board to work with the current 5 button control.
I am still no AC expert by a long shot but I sure learned a few things to this point and appreciate the help here.