New GFCI outlet; green light is on but no power
The key is that is the Leviton GFCI is lit green from the start it means its wired wrong. Counter-intuitive but true. Had the same problem and some searches finally told me this. I switched both sides top to bottom and bottom to top, and the light flashed red and then went off. Reset it and it went green and THEN I had power. Guess Leviton is wired opposite of others. Remember though, don’t switch left to right...just top to bottom. Black to brass, white to silver.

Just to help clarify: Read where the live and load are on the old unit and which wires go where, then read where live and load are located on the new unit and wire it the same.