Most Motherboards have a Front Panel connection that you can hook up to a switch/button Check out this example The Power SW is the power on switch. You wouldn't need the HDD or reset switches, just one for the power. So if you wired that to a push button you would be able to power on the machine that way.
Thats how I do it on all my PC based arcades.
Depending on where I mount the power switch I will also enable the power down on press option in windows. This can be a bad idea though if the power switch is in an area that someone can accidentally press.
Do you know what mother board you are using?