Here's the Nokia 6124c display backlight LED not working problem and shows a dark screen display when the device is turned ON. This solution provides some simple steps on how to fix such problem and show the components location on the PCB board including the display LED light connection tracks.
If encountered display light failure, you may first try to install or replace a working LCD just to easily determine or confirm if the LCD's backlight LED's is already damaged or not. And then after ensuring that the LCD backlight LED is still working, you may then refer to this solution below and do some check up procedures.
Nokia 6124c LCD Display Backlight Jumper Ways - Connection Tracks
You
may first trace the connection line paths of the LED's positive and
negative supply voltage from the LCD pin connector down to the
components where it is being connected such as the resistor. The LED
driver circuit is composed of chip transistors, and controlled by the
BETTY IC. The 3.7V battery voltage is also needed to make the circuit
works, you may read this voltage at the filter coils terminals.Note: The LED driver circuit also been used on the keypad backlight LED, if the keypad backlight is working OK and only the display LED were not, the problem may only possibly lies on a broken or cut-off display supply voltage connection.