Here's the service manual for the Dometic A/C's and Heat Pumps. It has a huge troubleshooting section for Roof mounted Heat Pumps starting on page 82. Bryant RV also had the manuals for either the 4 or 5 button thermostats
here (about 2/3 of the way down the page, this is the same place I linked for the service manual). Hopefully this will get you started.
Good Luck!
Stewart