No display LED backlight, how to fix?

Hi, your retina MacBook does not have an inverter - inverters are for old A1181 MacBooks and MacBook Pros which use CCFL tubes to light up the screen, which require an AC to DC boost inverter to power the CCFL. If you have tried resetting the SMC and PRAM and still have no luck, then the problem is most likely with the logic board. You can check around the display connector for any burned/dirty looking pins/corrosion, and try to clean the area, but you will most likely have to pay for logic board repair. I would suggest going to a reputable repair shop that specializes in component-level motherboard repair with a no-fix, no fee system, as it will save you lots of money. Apple on the other hand will replace the WHOLE motherboard, when it is only a small component on the board that needs to be repaired. The problem could also exist in the display assembly, but this is unlikely. If so, the store will notice this issue and suggest a screen repair instead if this is the case.