Just to say that testing what you believe to be a faulty cpu in another computer will not harm or damage anything.. (realistically it could, however the chances of it doing anything is HIGHLY unlikely).

I suggest that what you do is you take the cpu that you suspect is not working and put it in your other computer that you know IS working, if it boots up fine, its not your cpu..

If it doesnt boot up still.. then it is the cpu as your pc was working before with your other cpu..

Now if it does work in your other pc, that means obviously nothing is wrong so what you need to do is try the memory as everyone has suggested, remove all the memory from your system that is not booting. Now if you try each peice of RAM that you have, one at a time.. (obviously you can only do this if you have 2 or more peices of Ram / Memory in the computer)

If you only have the one stick of Ram / Memory remove the Ram that has always been in there, and try a peice of the Memory (if compatible) from your other computer (which you know works with it)

Then if the computer doesn't boot still, even with memory that you know works (because it works in your other machnine) then it's another problem, most likely a faulty motherboard..

Recap
So put the cpu thats not working into your pc that you know works.. if the pc runs.. the cpu is fine, so you need to test something else such as the memory (as talked about above). If the cpu does not work.. then you know its fucked.