|"my PC can't read the floppy without an OS"|
A BIOS update isn't going to help, but regardless, you don't need an OS to do the update.
Make sure the floppy is listed 1st in the boot order. Then boot off a WinME boot floppy & select "minimal boot". After it stops at the A:\> prompt, eject the floppy & insert the floppy with the new Dell BIOS on it. If the BIOS file is something like 4600_A02.exe, simply type 4600_A02 at the A:\> prompt & press ENTER.