I would say try cleaning the LCD cable connectors from the logic board and the LCD screen itself and at the same time try reseating them and hold the power and home button at the same time for 15 seconds and try turning it on again.
It could either be a faulty screen or the backlight component(s) on the logic board have become broken.
No signs of any physical damage on the LCD screen correct? Well since you can still see display but without backlight I'm leaning more towards logic board component damage like I said before.