WHAT THERMOSTAT MODEL????
Reset the thermostat and it is now in OFF mode, is the outside compressor off, is the fan off?
If so, go to COOL mode and lower the target below the room temp by 2F and the compressor and fan should come on; do they?
now increase the target 5F above the room temp and the compressor should go off. The fan may run 1 more minute.
If the compressor does not go off, disconnect the Y (compressor) wire and it should shut off. If it does not, the thermostat is not the problem as all the thermostat does is connect RC to Y to turn the compressor on and disconnect RC and Y to turn it off.
When the thermostat turns on the COOL, the word COOL on the home screen blinks when the back light is on; when the thermostat turns the cool off, the word COOL quits blinking on the home screen with the back light on. There is no blinking with the back light off.