Power doesn't run through the keyboard until the computer is on... so even if you managed to flash the firmware inside the keyboard to do what you want you still couldn't turn it on. You can turn it off once it's on but not the other way around.
But you could always mod a keyboard to house a power on button and have the wires run into your case from the back and onto the mainboard like normal.
Go into BIOS, under the Power management section.
In there somewhere should be an option to enable KB-ON or something like that. Maybe check your motherboard manual for precisely where this would be.
ATX power supplies are always on. When you press the power button on the front of your case, you're sending a signal to the power supply to power on the system. The supply was already receiving power though.
With the Keyboard power-on option enabled in the BIOS, the keyboard is kept powered when the PC is shut down, so that a keypress will turn on the computer.