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?
copy bios file xxxxxx.fxx onto USB thumb drive. turn pc on, press delete to enter bios. In bios, press f8 to enter built in flash utilty. Select update bios from disk. the USB key should come up as a HDD. Select hte xxxxx.fxx file and it will flash like u are using a floppy.