You could use a FLIRC and harmony / URC 7960 the FLIRC being set up to the power button causing a wake power on usb. ( the system will need to be put to sleep though, not fully powered off )
Is this hooked up to a TV? you could also look at having the a cec adapter set up so that when you power on the tv it would automatically turn on the pc. ( the ps4 has this built in now called wake on hdmi ) it's actually pretty cool. again though, this would need to be in sleep, not powered off.
Im sure it could be done with the system being powered off somehow but it would be quite complicated imho in the electrical department.