Well, it could be the Inverter, the cable from logic board to inverter, the LCD backlight or, in a percentage so negligibile that I'd not even count that possible, the capacitor on the Logic Board that fuels the Inverter.
Were you, I'd try with a fresh inverter. If that doesn't work, with a new inverter cable. Failing that, a new LCD panel.
I've got a Macbook 13'' myself whose backlight is slightly acting up, and I plan to fix it among some other "old age issues". They told me about desoldering the CCFL lamp and putting a new one, but that's a difficoult operation, so many people just swap a fresh LCD panel.
But as the LCD is the most costly part of the trio, you should first try with the inexpensive "Inverter + Inverter Cable" combo. Works 95% of the time.
It also would be useful if you gave us the last four letters of the Serial number, to gauge which model is the machine.