Yeah, this can happen. I had the same thing happen about 2 weeks ago. Nothing would come up on screen. Tore the computer down to bare bones and got nothing. Bought a new motherboard a week ago, and put it all together this past sunday, and everything is good!! Didn't even lose my HD info.
Don't despair. First check the video card. If you have a spare or one you can borrow from someone, use that to double check that the video card is not the issue. Then do as Monkey King says.
If you don't have a internal speaker (i didn't), then cut down to just the basics. Processor, MoBo, 1 stick of RAM, and Video card connected to the monitor. If this doesn't work, odds are you are gonna need to replace something. As to figuring out what to replace, if you can try different sticks of RAM, you could get RAM replacement ruled out. And assuming you already have the video card ruled out, that means CPU or MoBo will need replacing. I would advise replacing the MoBo first because it is usually cheaper, and CPU's are usually very reliable. Check
Newegg, and make sure and get a MoBo that is compatiable with your processor's type (P4 Prescott, w/HT etc.) and socket size (Socket 478, LGA775, etc.) as well as matching the speed of your RAM (DDR2-4200, etc).
BTW, someone gave me advice to remove the battery that gives the BIOS power. You might try that if you are down to no other options.
Jam it back in, in the dark.