DIAGNOSIS The Y (cooling) signal is not reaching the outdoor condenser. Usually a loose Y wire at the thermostat or air handler, or a tripped outdoor disconnect.
FIX Check the outdoor AC disconnect switch (the box near the unit) and the breaker. Ensure they are on. At the thermostat wall plate, verify the Y wire is securely under its terminal screw. The wire should be yellow or blue.
IF THAT DIDN'T WORK The issue is at the air handler. The Y wire may be disconnected from the control board there, or the contactor in the outdoor unit is failed. You need a multimeter to test for 24VAC at the contactor when the thermostat calls for cool.
HEADS UP Running the indoor fan without the compressor for extended periods can freeze the evaporator coil. Turn the system to OFF until this is fixed.