Is your problem no BACKLIGHT or no IMAGE?
Also, can you see the screen "activate" when it comes on? Meaning, when the laptop comes on, you can see the little ting that looks like ink moving around inside the screen?
You should have 3.3v on pins 2, 3, and 4 of the LVDS connector, and 27-40 on pins 21 ad 22.
If you have 0 volts on pins 38/39/40 you blew a backlight fuse. if you have 0v on pins 2, 3, or 4 you either got an F'd logic board or messed something else up that will be a PITA to solve.
Get measuring and let's get started.
EDIT:
Nevermind, I see you see an Apple on the screen. Just no light.
So we have two possibilities here.
a) You blew the backlight fuse, 0v on pins 21/22 of LVDS. If you have 0v here, 99% chance you F'd it up.
b) The board you got is a POS and not boosting. If this is the case, you'll see 12.6v on pins 21/22 of the LVDS connector. This means the fuse is intact since it is sending the main power rail through to the screen, but U9701 Is not using the inductor to boost it to the level required to power the screen. In this case. If this is the case, they sold you a faulty board, file chargeback and send it back. Or fix it if you want to, I'll help walk you through it, but this won't be easy or fun if you are new to this and you really should be reimbursed for the wasted time.
From what you posted this is an 820-2530 board, LP8543 Based, so there is a fighting chance of making this work. No proprietary APP001 BS!