Please, provide us with the last four numbers and letters of your serial number. You can find it in system profiler.
And well, an ailing backlight usually stems from three reasons and half, since the fourth is so rare to be nonexistant:
1. A bent/worn out/damaged inverter cable, the cable running from the logic board to the Inverter Board
2. A worn out/aging Inverter Board
3. A worn out/aging CCFL lamp in the LCD (that also causes dim tones and pinkish/yellowish hues when the LCD is on).
4. The capacitors on the logic board, the ones close to the Inverter Cable (rare, really rare issue)
That means that the usual troubleshooting requires replacing the inverter cable and the inverter, and, failing that, swapping a new LCD panel.
You could also attempt to replace the CCFL lamp in the LCD, but that would require a painstalking work of peeling off the reflective film behind the display, avoiding to crimple it, desolder a thin lamp (imagine it as a neon, for a visual reference, just thin, very thin), resolder a new one, cross your finger and recheck everything.
The suggested order is:
1. Getting a new Inverter Cable, from a reputable source
2. Getting a new Inverter.
Failing that, a new LCD.