Check mode and setpoint
Incorrect mode, fan settings, schedules, or temperature setpoints can look like an equipment problem.
Power and connection issues
A blank display can involve batteries, power, wiring, or system controls depending on thermostat type. Avoid touching exposed wiring if you are not qualified to work on it.
The thermostat may not be the only cause
A thermostat can call for heating or cooling correctly while the HVAC equipment still fails to respond. Persistent problems need system-level diagnosis.
Safety note: If you smell gas, see smoke or fire, suspect carbon monoxide, or believe there is an immediate safety danger, leave the area as appropriate and contact the relevant emergency or utility service. Do not treat an active safety emergency as a routine HVAC appointment.