If both the screen and keyboard aren't lighting, the issue will be with the backlight boost circuit (most likely the backlight IC).
You would require a schematic and board view for your particular board to diagnose this (board number etched on board, Google to find the files). You will also need a multimeter to measure the backlight output voltage (to see if this is the issue) and a hot air station (if it is a backlight IC problem, since it is a BGA chip).
Get the files and equipment if you think you can do it, then let us know when you are ready to check this. If you feel it may make the situation worse, it may be best to send it to someone who fixes these on a daily basis.