If ever encountered this problem and then tried installing a new LCD screen module but still a dark screen display occurred and the backlight LED doesn't light up; This solution below shows the circuit components that holds the Nokia 5130 backlight LED.
Solution for Nokia 5130 LCD Display Backlight LED that Does Not Working
You may check those corresponding components highlighted on the solution above.
Trace each particular line paths and check the supply voltage.
The LED driver chip when damaged will shutdown and all backlight LED's unable to light up including the keypad backlight LED's.So if both keypad and display backlight failed you may then suspect that the problem lies on the LED driver IC. But first, check the supply voltage and filter coils before attempting to replace it.