UPDATE: Just got my BIOS to work!
Here's my workaround:
- Turn your power supply off and unplug it from the wall.
- Unplug EVERYTHING from your PC, except your keyboard. By everything, I mean all USB devices, all SATA cables, your GPU (if you have on board graphics), and everything else you can possibly unplug.
- Remove the CMOS battery completely.
- Connect your monitor directly to the motherboard (again, if possible)
- Plug you PSU back to the wall and turn it on.
- Turn on your computer. Since you don't have any SATA devices available, it should go straight into BIOS.
That did it for me!
Don't forget to plug your CMOS battery back on after you get it working (turn off your computer first).
After some experimentation, I found out that the culprits were my SATA devices. I can get to BIOS simply by removing each and every SATA cable from my drives. I have absolutely no idea why!
Since I still can't get to the BIOS with my drives connected, I won't consider it solved... But I hope it helps someone else!