CPU Startup problems

Here is my problem. I have a PIII Intel 800 CPU, 133MHZ. Now when I boot up my PC the first time it works fine. If I do a restart or reset it works also. Now here is the problem, when I do Shutdown and power off the CPU, when I press the button to Start up the computer it starts for 2-3 seconds and then the power shuts down. The only way to make it work is by unplugging the Power cord behind the cpu, wait 10 seconds and then plug the power cord back and power the PC!!!!! I’m I forgetting something in the Bios SETTINGS???? I even went as far as changing the Motherboard and the power supply but I get the same problems.