The fact that it displays to an external monitor fine suggests that the video display card is fine. From my experience, the issue is likely with the LCD/LED panel itself or the ribbon cable to the LCD/LED. However, a quick Google search on your issue contradicts my thoughts and suggests that it is likely a motherboard issue. So, given Kris' findings as well, I will go with motherboard too.
Have you tried clearing the CMOS and adjusting brightness or backlight settings in the BIOS? Not sure if you were doing that in the OS.
Something free to try: Remove the battery and AC power for 20 minutes, then press and hold the power button for 15 seconds. After this is complete, install the battery and connect AC power, then power on see what happens. This is supposed to perform a reset