If you are faced with a computer that will not behave itself, the first thing to do is decide if it is a hardware fault, a software fault, or - if you are reall lucky - a mixture of both. First, lets look at a 'dead' computer.

Dead Computer 

If the machine is completely dead then the first thing to do is check that it is getting power - which means making sure that it is connected to a mains supply (or if it is a laptop, that the battery is not dead). Check that the mains lead is well seated. Check that the fuse has not blown. Check that there is power to the socket. If you are sure that the supply is OK, then the most likely fault is the computer's power supply. If it is a laptop, there could be something wrong with the transformer, or the batteries may actually have failed. If the machine has made a 'fizzing' noise, or there is a 'bang' when you apply mains power, or an interesting electrical smell in the air - then it is very likely that the power supply has failed. More than once I have turned a'fizzing' machine off and when it was turned back on again it has failed with a spectacular 'crack!'.

If the power supply has failed - then you have no choice but to replace it. If you are lucky, it will not have fried the main motherboard. Power supplies can be purchased from many sources - but make sure that you obtain one that is the same size and shape, and which has the same power output as your old one. Replacement is straightforward - but make sure that you note where all the connections are inside the machine BEFORE you disconnect them.