A window air conditioner has two jobs: move air and remove heat from it. When it does the first without the second, the fan is fine and something is stopping the refrigeration side from doing its work. On an LG window unit the list of causes runs from the trivial to the sealed system, and the order in which you check them saves both money and risk.
Mode and Delay
Confirm the unit is in Cool mode rather than Fan or Dry, and that the thermostat is set lower than the room actually is. In Energy Saver mode the fan cycles off with the compressor, so a unit that seems to stop and start is behaving as designed. After any restart the compressor waits a few minutes before running, and during that delay the fan blows room-temperature air. Give it time before concluding it will not cool.
The Filter
A filter loaded with dust chokes the airflow across the indoor coil. The coil gets too cold, moisture on it freezes, and the ice blocks airflow further, until the unit blows a thin stream of barely cool air. With the unit switched off, open the front grille or filter door, slide the filter out, wash it in warm water, let it dry and refit it. If the coil behind it is frosted, leave the unit running in Fan-only mode for an hour to melt the ice before returning to Cool. Wash the filter every couple of weeks in season, more often in a dusty room or a home with pets.
The Plug
LG window units are fitted with a cord that has Test and Reset buttons on the plug body. That is a leakage-current device, and it trips if it senses a fault or sometimes after a power surge. A unit that is completely dead often only needs the Reset button pressed on the plug. Press Test afterwards to confirm the device trips and Reset again to restore power. If it trips repeatedly, there is a real electrical fault and the unit should stay unplugged until it is checked. Never run a window unit from an extension cord or a power strip; it needs its own outlet.
The Outdoor Coil
The rear of the unit rejects heat through a second coil that collects dirt, pollen and cottonwood seed. From inside, with the unit unplugged, look through the rear grille as far as you can see; a coil matted with debris cannot shed heat and the unit runs warm. Removing the outer cabinet to clean the coil properly exposes the compressor and its start capacitor, so that cleaning is a job for a technician or for the unit's annual service, not for a rag through the vents.
What Points at Refrigerant
A clean filter, a clear coil, a compressor you can hear running and air that is still not cold usually mean the refrigerant charge is low or the compressor is not pumping. Frost that forms on the copper pipe rather than across the coil face is another sign. None of this is owner territory: Section 608 of the Clean Air Act requires EPA certification to open, recover or charge a refrigerant circuit, and there is no owner-serviceable valve on a window unit. A technician can weigh the decision between repair and replacement against the age and size of the unit.
Booking a Look
Note the model from the plate on the chassis, whether the compressor starts, whether the plug has been tripping, and what the coil looked like behind the filter. Book an LG air conditioner repair with those details.