Eh, I started at the thermostat because I'm a systems integrator and the first problem solving step is "Turn it off and on again". When I flipped the 'heat/off/cold' selector lever on the thermostat to 'off', the LCD display declined to switch off the 'heat on' section. If you touch the non-touchscreen display it spazzes out, and so does attempting to access the user or installer menus.

Lastly, the furnace would work correctly if the thermostat was popped off the wall, batteries popped out, then replaced on the wall until it reached the demand temp. Once it got to the demand temp first time, it would stop working again until the thermostat got power cycled or at least removed from the wall again.

But really I just tried to turn it off and on again and it wouldn't turn off properly.

And I may have misread your comment. If you're talking about establishing the wiring patterns, I can sort of see that, but on the other hand it's kind of like going back to the patch panel to see if it's wired for 568A or B instead of just looking at the socket you're switching out. Feels like a wasted effort if everything in the wall box makes sense.