Answer: Hack together a USB dongle that does nothing but F1.
I admit that this is a silly problem and an even sillier solution, but the mind boggles at the possibilities: custom keypads for gaming, a Control+Alt+Delete "easy" button...
...any key or combination of keys can be broken out into an apparatus as keyboardy or keyboardless as you like, and used to do anything a keyboard can do!
Step 1: Why?
Well, you are absolutely right (though calling me names was kind of mean).
The problem is, I'm building a publicly-accessible PC kiosk (mouse only, no keyboard), and the components are squeezed into a rather small space. The donor PC featured a very tall heat sink/fan that just wouldn't fit, so I had to swap it out for a smaller one. The problem: the original fan was a four-wire model that talked to the motherboard, telling it soothing things like "I'm working." The replacement one I had on hand was a two-wire fan that refused to discuss anything with the motherboard. So on startup, the bios would report a failed CPU fan, and stop at a prompt: F1 to continue, F2 to enter startup... so my kiosk would sit there waiting for someone to press F1, and would be the lamest kiosk in history.
Of course, some of the warnings that show up during startup can be turned off in the BIOS (like the "keyboard error"), but my BIOS had no option for "don't worry about the CPU fan." If I knew more about the world, I may have been able to grab the two unused wires from the CPU fan swap, and add a resistor or some other little bit of hardware that would fool the motherboard. Instead, a dim light-bulb flickered above my head, and I performed the following test:
Plug in a USB keyboard, hold down F1, start PC, keeping F1 pressed.
I watched as the error popped onto the screen, then vanished.
The OS loaded fine, the browser opened fine; no "Help" pop up... in short, no ill effects from holding down F1.
So I assumed that the OS was smart enough to accept the F1and then ignore a "stuck key," and I decided that my silly plan was worth doing.