If your Lg air conditioning unit won't come on at all, then you should check the thermostat. Turn off the power at the wall before doing any investigation. Firstly, ensure that there is power to the thermostat, both by checking the wiring supply to it, and also by replacing the batteries. Try turning the power on again. If nothing happens, turn power off and proceed. The next thing to do is to check that the thermostat is clean, and that it is not faulty. The latter can be done by turning the power on, setting the thermostat, and watching as it goes through the motions.
Is the unit simply not working at all, is it not cooling the air much, or is it simply blowing around warm air?
the condenser (for an outdoor unit) or air handler/furnace (indoor unit) are not running.
Make sure it's plugged in. This may seem obvious, but there are occasions when this is exactly the problem. Whether kids, dogs, or an accidental tap with the vacuum cleaner, the plug could be partially or completely dislodged.
Check the circuit breakers and fuses. Make sure they are in place, turned on, and functioning properly. Circuits, especially with older homes, are easily overloaded if the AC shares a circuit with appliances such as irons, refrigerators
Check your thermostat (cooling control) and make sure it is set to cool at the current temperature, and working properly. As with plugs, sometimes settings can change by accident.
This can cause low air flow which allows ice to form, and thus causes low cooling performance.
Repair or replace the blower belt. Allow the ice to melt before restarting the Lg AC unit.
If they are caked with dust and debris, clean them thoroughly. Make sure you let any ice melt before restarting your Lg unit.