Blank Screen, on MOST boots

I have a Toshiba Satellite P100 laptop, that has low hours on it. It is 5 years old. Starting a couple of months ago, when I would boot it(LEDs and hard drive would appear to boot fine) , the screen would be blank(not illuminated black). If I would try again, it would work every 3rd or 4th time. This stretched out to every 20th time.
I read online about removing the battery, and disconnecting the power cord from the laptop, then holding down the power button for 60 seconds, then reconnect the power. This works occasionally, but seems too random to be sure.
Anyways, what the heck is wrong with the laptop? I can't see it being the backlight (or some inverter related to..), as if it were burned out, it wouldn't occasionally work.
Could it be a lid switch or broken wire to the lid?

I hope this is where I can ask a question, as the toshiba.ca site sucks, and when I phoned, all they did is give me an address to a service depot.

 

have you got an external monitor you can test it on? if it works on the external monitor then the screen has a connection issue or similar.

if it fails on the external monitor also it could be all sorts, memory, HDD, cpu, gpu etc etc