Never had an issue like this but……
Your problem could be a short: have you put any screws through the wall(hanging a picture)…or could wires have gotten pitched together from a slide. An easy check would be to disconnect the wires from thermostat and see if the signal wire has constant power(with fuse for furnace installed). Or a better check would be at the circuit board to see if it is constantly getting a signal(power)to run. If there is no short you should be able to eliminate that part of system.
Boards can come bad and it can be a headache wanting to believe it can’t be bad.
My mom would say, “it’s a ground problem”. Over the years she has seen my dad and I chase so many electrical issues that turned out to be a ground issue. Mom is right more times than not.
For me, when trying to chase electrical issues, I slow down and think of the system. I get as much paperwork as I can(schematic, wire diagram, trouble shouting from manual, warranty, and manufactures phone number for technical issues…..) and then start chasing.
This forum is a great source of personal experience but might go straight to calling the manufactures technical support. These guys are usually very nice and can give a direction to look.
2011 Wildwood T26BHXL
2004 Yukon XL Denali
43yrs of camping; one lucky guy