I agree with cmeeks answer. Your video card is very likely at fault.
Does the monitor come on at all even when you first turn the PC on? Do you see the BIOS screen or Windows loading screen?
If you don't see even that much, then besides cmeeks advice, I would also try reseatting your RAM chips. Just be sure that there is no power going to the PC before you start disconnecting/reconnecting anything.
If it all works again but locks up/freezes after a while, then again, think about fitting a new graphics card as this is most likely your problem (though don't rule out the RAM either, especially if its an onboard graphics solution you have).
Hope this helps!