I have a emachine that when you turn it off it will turn it self back on. I put in a new power supply. I still continues to do the same thing. I disconnected the power button and plugged in the power cord and the computer came on. Could the motherboard be damage? I also reinstalled the o/s windows 98.

Where did you disconnect the power button? The front power button connects to two pins on the motherboard. Pushing the button simply momentarily shorts those two pins together, causing the motherboard to signal the PSU to power up. If you disconnect the wires from those two pins and it still does it, then you know the button itself is not defective. Be sure to power down, unplug and touch bare metal to discharge any built up static in your fingers before reaching inside the case.

Look in the BIOS setup menu for the various power on or boot on settings. Most BIOS setup menus allow for the option to boot up the PC when a signal is received via the modem, network interface card, keyboard press, and/or mouse movement. Ensure all those are disabled.

If all disabled, then I would suspect the PSU or motherboard.