Why is my laptop not starting up

I have a toshiba satellite c660/c660d which will not start up. Last week I had the same problem with it so I left it on charge then a day later I tried to put it on again and it started working fine, but now it is doing the same thing again. The fully chared light is on when charger is pluged in, I have taken the battery out and charger out and held the power button for 30 sec then put the charger back in and tried to start it but all it does is put the power light on and you hear the fan for 2 sec then stops, if anyone can help that would be great thanks
 
3-4 year old machine. If never cleaned inside, you should probably do that - a hidden blanket of dust could hold heat in causing machine to halt rapidly if temps rise. Look up videos on YouTube for your model, etc - clean inside fan shroud too.

Among several others:
 
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