the real question is, why would you want to do this? If you are worried about someone using the cabinet without your permission, it would probably just be easier to have the power switch mounted inside the coin door or something, so you have to have the key to turn it on.
if you are dead set on having a boot password, i guess it depends on what encoder you are using for your controls. if it is a keyboard based encoder (ipac, keywiz, x-arcade, etc) then it shouldn't be an issue at all. you would use your keyboard to get into the bios setup, go to the place where you configure the boot password and then use your controls to input it.
however if you are using a gamepad or similar interface for your controls (hacked gamepad/joystick, gpwiz, etc) then this will not work.
either way, it seems kinda pointless.
as for the comment about having to press F2 or Del to enter the bios, that is only to configure the bios, i believe the original poster was referring to setting a password to get the PC to boot into windows, not the password to configure the bios. this would not require you to press any additional keys. when the pc powers on, it sits at the bios screen and waits for you to enter a password before proceeding to boot the OS.
and to Digital Vandal, bios passwords aren't dangerous, like DJ_Izumi stated, all you need to do is clear the cmos (usually a jumper, or remove the battery) and the bios password is gone.