Hm. So no way to enter BIOS without first loading the drivers, which are loaded only by booting a full fledged OS. This implies that even if you were to access BIOS in its' native environment you would not be able to do... anything. That rules out forcing POST, as well as any method that would give you access to the native BIOS screen. Which is about 95% of solutions. Hm. You are in quite a pickle here, I must say. This leads to only a few solutions, most of them pretty far fetched and neigh impossible.
1) As previously mentioned, edit BIOS and flash said BIOS to the motherboard. Risk corrupting BIOS and locking yourself completely out of.. everything in the process.
2) Edit BIOS AFTER loading a GUI based OS that enables the USB drivers - IE the keyboard. Only in certain circumstances is this even possible, and generally it is tied to specific parts of the BIOS, such as AMD Overdrive or RivaTuner. (Does RivaTuner even still exist? I haven't used that since the Radeon 8500 and the Ti4200 were the GPU Giants....) Only in one or two cases have I ever heard of the possibility of having near-full access to BIOS's settings from INSIDE the OS, and if memory serves they were either custom built motherboards specifically for the "master nerds" and top notch gamers, or a rare consumer motherboard. Even then I couldn't verify that it actually did exist, I don't remember if this was a story I heard from an unreliable source or an actual posting on a site such as this. It was some time ago.
3) Probably not going to work. Highly doubt that you could flash a UEFI bios onto that board, or that the board supports UEFI to begin with... But if it did you could install Windows 8. Inside Windows 8 is the option to boot FROM Windows INTO the BIOS. I don't know if the drivers activated carry over through the reboot, but worth a thought. I'm basically spitballing any hairbrained theory that creeps into my head in a hope that one of them work. That's generally how I solve my own problems, trying the most random, far-fetched things you can think of that still retain some logic until one works. Then I remember it
4) Running out of steam here... Lemme think.... Well, there's the obvious. I'll go ahead and say it. Get another mobo xD.
I don't know if any of the above would be possible to pursue for you. Without access to the native GUI for the BIOS, editing any values in BIOS is basically impossible, unless the BIOS itself is designed otherwise. Hmm.... Final thought...
I don't know much about virtual machines, never set one up myself. But my understanding is that you can boot from the beginning inside a virtual machine, while retaining full function of the initial OS, IE all the drivers and such. Might be worth researching.
That's all I got.