Chosen Solution
I have the Toshiba 39L1350U and when powered on, the top left of the backlight turns on for maybe 0.5 seconds then shuts off and the whole screen is dark, but if I shine a light on it I can see menus so I know the display is working. Does it seem like a LED, power supply or main board problem?
@zero_smith by the symptoms that you describe, this is a failed backlight array. You can replace the backlight strip by tearing the panel down. Not a bad job but you need to take your time and do not flex your screen :-)