DIAGNOSIS: Your thermostat is sending the signal, but your outdoor condenser unit isn't turning on. This is usually a power or pressure issue with the AC side of your system.
FIX: Go outside and check the condenser unit. Listen for a hum and look to see if the fan on top is spinning. If it's silent, check the exterior disconnect switch (usually a small box on the house wall near the unit) and the circuit breaker for the AC. Reset both. If the unit hums but the fan doesn't spin, the capacitor is likely bad—this requires an HVAC tech.
IF THAT DIDN'T WORK: The thermostat might not be configured correctly for your system. Go to Settings > Installation Settings > Equipment > Reconfigure Equipment and walk through the setup again, ensuring you correctly select AC, Heat Pump, etc.
HEADS UP: Many systems have a 5-minute compressor delay after a power cycle or previous cycle. Wait a full 5 minutes after restoring power before declaring the fix a failure.