So there were two not so good looking components in the area around the LCD connector close to the backlight IC. Darkened capacitor, i replaced it. And one little darkened core-ferrite bead which i also replaced. And problem solved! The LCD lit up! I believe that the core-ferrite bed was bad, because its functions are to block noise for the backlight IC.
The home button’s flex cable caused the problem, because i tried connecting only the LCD and it works fine, but when i connect the home button to the board, the phone immediately goes off, or when i connect the cable while the phone is off it doesn’t turn on. Now i saw oxidation where the home button connects to the flex cable on the back side of the screen.