New LCD screen and still no backlight

Leo, the iPod Nano is a habitual trouble maker with the back light. I know that the 4th and 5th gen are some of the worst ones. Now the backlight is actual part of the LCD that you already replaced. The inverter circuit is on the logic board. I have never managed to isolate the coil that is responsible for most failure on the Nanos. So the only thing that I can think off right now would be to make sure that the cable is seated properly. To clean the cable and all the connectors and clean the logic board with isopropyl alcohol as outlined on here If the backlight coil on your logic board got shortcircuited, that may require a new logic board. Can you see your iPod very dim on the screen (hold it at an angle and shine a light across the screen. If you still see your iPod menu etc, you will need either a new logic board or isolate the coil. If none of this works for you, You may just have to replace the logic board. Hope this helps, good luck.