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Did you allow the new T'stat to program itself before trying to activate it? You may want to reset the T'stat. Make sure the switch is in the off position unplug the T'stat data cable, wait a minute and then plug it back in. If I remember correctly you push the mode and zone button simultaneously (Do Not Turn On the T'stat) and wait for it to find all the parameters. To answer your questions, the furnace does get its control power from the roof units.
Mike, RVIA & RVSA Certified Master RV Technician
Amy, Dr. Assistant - Roxie & Mei Ling, four legs each
2000 Gulf Stream Scenic Cruiser 450 hp & 1330# torque
06 Saturn Vue, 06 Chevy Z71 4x4 & 2014 Corvette Z51 M7