How old is the computer? How old are the hard drive and optical drive? What operating system do you have installed? Do you still have the original set of install/bootup disks?
First, we need to determine what might have failed: memory, video graphics, hard drive, power supply, or heat failure of CPU from too much dust and pet hair.
Does anything at all light up when you push the <ON> button? Do you hear any beeps, or other noises? If not, look at the fan blades in the power supply to see if they are turning after you press the <ON> button, or if they only turn 1/4 to 1 turn then quit.
If they are continually turning, then the power supply is good. If they turn one rotation or less, the power supply is bad.
If they are turning continually, then next attempt to boot in SAFE MODE, by repeatedly pressing the <F8> button about once per second as soon as you press the <ON> button. This will usually enable the computer to boot up in SAFE MODE even if the video graphics card is failing.
If it is a memory module that has failed, it mayl not start.
remove one memory module is there is more than one, then try starting. If that doesn't work, try the other memory module.
If it is a hard drive, it might not start.
Do you have a floppy drive in that computer? Can you borrow a floppy disk from somebody who has a Windows 98 or Windows ME boot floppy disk. If so, disconnect the hard drive power cable to see if it will boot to the floppy disc.
If no floppy disk, attempt booting to a Windows CD Disk with the hard drive disconnected.
You may need to go to the BIOS to change the boot order, but that is difficult to do when it won't boot.
Do what you can, from the above list, and get back to us with more details about the configuration, and what does or does not happen when you attempt to turn it on.