Toshiba....
Also had a toshiba, they seem to have some funny problems. To the OP: if it is some hardware problem better take it to be fixed, but before you do try to turn it on after clicking in the button and if notthing happens, simply give a small bang between the keyboard and the screen (at the side of the "turn on/off" button).
This may seem stupid but it works... Toshiba's from a few years back tend to have some electro static interference that can be solved quickly with small bang. You will punish the laptop and it will work!