Try plugging a monitor into the VGA/DVI port on the laptop, if you get the same thing on the monitor it's the motherboard thats at fault, if it's not then it's probably the screen.
If it was only a cheap laptop and the screen is dead then it might not be worth repairing, when we change screens on Acer's at work they are £150-£250 just for the screen
Re Toshiba's, we get them in a lot for overheating, normally it's because the heatsink's Toshiba uses have very closely spaced fins that get clogged with dust really quickly, an air duster usually sorts that out
