Lg lwhd1009r the fan will not run?

Make sure the capacitor is good and that the motor is receivimg power.

Most window air conditioners run the fan all the time but cycle on and off the compressor that makes it blow cold air, I knew a AC that was a small Hunter Bay brand (which I think is LG) that shut fan off also when it reached the right temperature.

Hard to test them in winter, you may not have it warm enough in the room for it to start making cold air, generally speaking that could be the problem.