They don't get it do they? The screen is black. As in BLACK ;P
Look, it sounds like there might be a short-circuit or defective component somewhere. Make sure your PC isn't in touch with any other metallic objects, like heating or just anything underneath it.
When that (probably) doesn't help, then just do the following:
1) Remove ALL hardware components, harddrive, memory, video card, sound card, EVERYTHING. So that you have only the mother board. Note, either remember how everything was by writing it down or taking a picture, or be sure to have the manual of the mother board (you can often download those).
2) Add ONE bar of memory. Connect your Power Supply Unit to the mother board. (leaving the mother board screwed to the casing).
3) Try to turn it on. Just see if the case lighting is any different from when you have the problem - you may not actually notice a difference.... That's OK.
4) Connect the monitor :P and power it on again. If your monitor or PC has multiple connectors for the screen, try them all.
5) If it still fails, it could be that one memory bar - try using another memory bar.
6) If it still fails, it could be the monitor, try replacing it. - EVEN if it says no signal, the problem can be with the monitor.
7) Try replacing the cable between the monitor and the PC.
Throughout the whole thing, be very meticulous. Keep track of the steps you take and don't try to rush it. Just take your time to do it right. =]
Let us know how it goes! Also if you still need help if this didn't work. The forum is with you!