Ah, on my nForce4 board I can hit ALT+F2 at boot to get to the built in AWARD.exe BIOS flash program embedded in the motherboard.
Does the P35's BIOS have a nifty feature like that? If so you just put the newBIOS.bin file in the root directory and write the name of that file on a piece of paper (so you don't forget since you need to type it in) and boot into AWARD and type the command line and done.
I haven't used a floppy since nForce3 days, let us know if you have that feature, I don't feel like googling for hours either! Also, there are several on-line BIOS updating programs made by board makers, again my nforce4 board has such a BIOS checker program, it even checks my video card BIOS for updates as well, neat eh?