Chosen Solution
When the battery is empty, the logo shown on screen is clearly visible with backlight on. But when i boot into the OS the backlight does not funktion and i need a bright light to see anything.
Your backlight control logic is messed up! See if resetting your SMC resolves it How to reset the SMC of your Mac If not, time to visit an Apple Store so they can reset it Do make sure your battery has a charge before you go
