Chosen Solution

Starts up normally it chimes, but screen remains black. When I aim a flashlight through the Apple logo on the back, I can see the desktop icons and the mouse cursor. When I connect an external monitor it displays normally after logging in. And not before that. I repeatedly reset the NVRAM and SMC, but it didn’t make a difference. I have another MacBook Air I attached the 31pin display connector to this one, and it showed the same issue on the known working display. Please help.

You’ve isolated the problem down to your logic board backlight circuit. Either the backlight driver logic or the fuse link are burnt. The question here is do you have access to the needed parts as well as the needed tools to replace this SMT components? There are a few outfits that do micro soldering and have access to the needed parts.