The solution below shows the keypad LED backlight circuit including its line tracks, for easy tracing procedure.
The LED backlights is driven by an LED driver which drives and boost up the current and voltage which make the LED lights intensity stable.
The LED driver IC become damaged or faulty will result to LCD display and keypad backlight LED failure.
Nokia 5130 Keypad Backlight LED failure repair solution
Check all LED first if it working or not, LEDs were connected in series so if only one LED become faulty may result that the others not to work.
Trace all corresponding line paths. Check the LED driver supply voltage, this voltage is 3.7 volts that came from the battery. Check all filter coils and resistors.
If all line paths an other corresponding connected components were both okay, then proceed to replace the LED driver IC.