Tripped Float Switch (Clogged Drain)
Float switch in AC drain pan tripped, cutting 24V power to the entire low-voltage circuit including thermostat operation. Even though thermostat display still works (it has internal power), heating and cooling won't activate.
Locate indoor air handler. Find drain pan and float switch (small plastic device with wires). If float is UP, it's tripped. Standing water in pan = clogged drain.
Clear drain line: wet/dry vac at outdoor end or vinegar in indoor port. Drain the pan. Reset float by lowering manually.