This is a power issue. The thermostat isn't getting its 24V from the system.
Start with the basics. Check your home's circuit breaker for the HVAC system and reset it if tripped. Verify the power switch at the furnace or air handler is on. Ensure the furnace door is closed securely; many systems have a safety switch that cuts power if the door is ajar.
If that didn't work, the C-wire connection is the most likely culprit. Go to your furnace control board. Find the bundle of thermostat wires. The wire connected to the C-terminal must be secure at both ends—at the furnace and behind the thermostat. If you used the included C-Wire Adapter, verify its installation.
If the screen remains blank after checking all connections, there may be a blown fuse on the furnace control board or a wiring fault. At that point, it's time to call a pro.