screen goes black (0 brightness) but computer is still ON

MacBook 13" 2.13GHz Core 2 Duo Mid2009 white

Hello!

My Mid-2009 white MacBook just started to present screen issues. At first the screen began to flicker, but it all was fine. Last night it turned black and I thought the battery was depleted but it was not, and I moved the track pad and saw the Dock magnification so the computer was on. I lowered the brightness with F1 and then increased it and it was there again. Two hours later it happened again, but now when going to 0 brightness and then leveling up it just stays on for around 10 seconds and then it is black again. If I keep the brightness level very low (just three presses to F2) the screen stays on around 10 minutes before the flickering comes and it shuts down. I have a base of fans so is not overheat I am sure. I am currently hooked to an external monitor and it all works OK, save the screen, but after an extent read, I cannot determine whether it is a problem with the display data cable or the inverter cable. Could you guys bring any light on which could be the most possible cause?

Thanks a lot!!