Hi,
I have had this problem before and there are so many reasons why it might not start. What i do is to take the ocmputer out of the case and put it on a table surface (this helps to make sure the motherboard isnt shorting). Has the motherboard got a 4 pin connector that looks similar to the motherboard connector? If so and your power supply does not have this connection is may mean a new power supply.
Or make sure that you have the power switch in the correct plug lol. All to often this is why a computer wont start. If you dont know which try them all. For a quick way you could just rub a screwdriver over the two pins at a time but this is not really recommended lol.
Hope this helps, Nick
www.nbpcservices.co.uk