Backlight not turning on after water damage. What to do?

Hi all, first time poster long time follower. I have a slightly water damaged MacBook Pro 15" early 2011 A1286 that was given to me. I was told it was caused by a bit of melting ice, the water got inside the casing where the DC-in board is located.

By opening it, I could see there was corrosion mainly on the DC-in board and a little around the the chips on the logic board on top where the USB ports are located.

Here's the thing, EVERYTHING works, it boots, sound works, ports work it charges when connected. However, the display does not light up. I can see what is on the screen under a source of light, the same as if when the brightness is turned down (obviously, I tried adjusting the brightness with F1, F2, without success). It does work perfectly fine connected to an external display.

I have since then cleaned the corroded areas with alcohol and it didn't change anything.

I have also noticed that there was what appear to be a small burn mark on one side of the display connector (on the metal part) and 2 of the pins on the cable are silver-ish instead of gold-ish.

I really don't know what to do to fix this baby up. Any thoughts/suggestions would be greatly appreciated. :)

PS: just for your information, I'd say i'm somewhat experienced in mac repairs, having repaired countless parts/devices. But never really ventured into soldering anything though, yet! I'm a bit worried it might come to this.