Do you know it is the thermostat versus a problem with your HVAC system? It is possible the thermostat is working fine and something else is not. Check the HVAC system. Look for lights blinking that normally don't. Often if there is a blinking pattern or a number or letter displayed it indicates a problem. The manual may be able to tell you what is wrong.
On the thermostat check settings like what kind of system type you have and fuel type. The thermostat often needs to know that in order to switch on or off the proper wire. Make sure the wires are properly attached at the thermostat and one has not come loose.
If you happen to have your old thermostat you could reinstall it temporarily to see if the system works again.
If you want a another pair of eyes to look at your thermostat wiring send an image of the wiring, ideally with the old thermostat and the new.
