The answer to this is it has a dry joint on the logic board due to the fan being dirty and the panel running a bit too warm. You can search for instructions as to pulling it apart and what you need to do is remove the top. Mark the screws as they come out otherwise you will be lost.
Next clean the unit remove the fan and clean that.
If you have top quality heat transfer paste its easier to clean if you remove the heatsink as well. DO NOT take the heatsik off unless you are able to clean off the old paste and replace it, or switch on without the heatsink.
Now with a clean unit, look for the plug on the left marked backlight, its near the top left corner. Down a bit, and in a bit, is a brass springy thing which I suspect is an earth for the touchpad. Now look across left, and near there is a tiny transistor. From the plug there is a small IC perhaps 4 pins one side and 2 the other, and below that is this transistor a 3 legged thing about 1mm square with the 1 leg side towards the screen.
That is dry jointed. With a fine pointed soldering iron press down on each leg and the job is done. Rob.