If you open the door and the lights don't come on you need to check voltage and polarity at your power source.
If you have lights the display should also be lite. Adjust your temperatures to 0*f in freezer and 36*f in fresh food.
Some LGs have to be turned on after a power failure. Usually the sequence of buttons to push at the same time is on the display or in the owners manual.
Next, pull out unit and remove the back access panel carefully. Is the fan next to the compressor running? If not, remove the access panel above the compressor. 3 screws hold it in place. BE CAREFUL this is the main control board and at some connections there is 300 + volts. You want to look for a blinking light. Count the number of blinks.
If no blinking light, unplug the refrigerator.
There is 1 sometimes 2 fuses located on the board. Check with a meter for ohms/resistance. You can gently pull the fuses out. They are about an inch long, round glass fuse. You can visually look for the broken wire too if you don't have a meter. The fuses have their size on them. Most hardware stores carry them.