Thermostat screen blank: is it the thermostat or the furnace?

A dead thermostat display is a power problem, and the power comes FROM the furnace. Half of these are furnace-side.

Batteries

If the thermostat takes batteries, replace them first, obviously. Many hardwired models keep a battery only for the display.

Furnace switch and breaker

Hardwired thermostats run on 24V made by the furnace. Furnace switch off or breaker tripped = blank thermostat. Check both before blaming the thermostat.

The furnace door safety switch

Door ajar cuts all 24V — same blank screen. Push the blower door home.

Blown low-voltage fuse

On the furnace control board there is a small automotive-style 3A or 5A fuse. A shorted thermostat wire (staple through the cable, pinched at the furnace) pops it and everything 24V goes dark. Fuse costs a dollar — but if the new one pops too, there is a wiring short to find; that is the technician version.

Condensate float switch (some setups)

A full condensate pan can open the 24V circuit on purpose. If there is a pump or float switch, check for standing water.

Safety line: Replace the low-voltage fuse once. A second blown fuse means a live short in the thermostat cable, and continuing to feed it fuses risks the control board itself.

Is the furnace flashing a light?

If the burners will not light, the control board is almost certainly flashing a diagnostic code behind the little window. Count the flashes and look the code up by brand here — walking into the phone call knowing the code saves diagnostic time.