This may happen and occurred if the device suffered water or wet damaged, heavily dropped and alike.
To fix such problem, you may need to replace the LCD panel, to easily confirm if the LCD screen is still working or not. After ensuring that LCD screen is okay, you may refer to the solution below for it shows the connection of the LCD white backlight LED circuit.
Nokia 6600 slide LCD screen white backlight LED failure solution
1. Have a new LCD screen replacements and then replace the LCD.
Check the lcd flex cable. ensure that cable ribbon is properly pinned to the connector.
Replace the whole ribbon cable assemblies if damaged.2. Check or clean the LCD pin connector.
3. Check the inductor coil, and read the VBAT (battery voltage) across to it.
4. Trace the connection line paths of the LCD backlight LED from the pin connector down to the capcitor and resistor where it is being connected. Check or replace also the said components.
5. Replace the backlight LED driver IC.
6. If all of the above doesn't solved the problem, in this level, you may need to rework the betty IC or then replace if necessary. The betty IC holds as the switching circuit of the LCD backlight LED.