The problem is one of four things:
1) Bad floppy drive
2) Bad floppy disk
3) You don't have DOS boot files on your floppy (
autoexec.bat, config.sys)
EDIT: MSDOS.SYS and IO.SYS, per BC_Programmer4) Improper floppy boot sector
- i.e.: you formatted the floppy using Windows Explorer in XP or Vista, but didn't select "Create an MS-DOS boot disk"
- in this case, the boot sector is not looking for
MSDOS.SYS or IO.SYS. It's looking for NTLDR, ntdetect.com, and boot.ini (for NT, 2000, XP, Server 2003) or bootmgr and boot\bcd (for Vista, Server 2008, Windows 7)
For #3 and #4, just select "Create an MS-DOS boot disk" and format away. Copy your BIOS files on the floppy afterward (if they fit).
For #2, try a new floppy.
For #1, either replace the floppy drive or use a USB floppy (just make sure the BIOS can boot from a floppy).
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On the other hand...
If you want to avoid using a floppy altogether, you could make a bootable CD that emulates a floppy.
1) Download VFD:
http://chitchat.at.infoseek.co.jp/vmware/vfd.html#download2) Set up a virtual floppy disk to use drive letter A. You may have to disable or disconnect your physical floppy drive for this purpose.
3) Format the virtual floppy. Again, remember to select "Create an MS-DOS system disk."
4) Add your BIOS flash utility and appropriate file to drive A.
5) Unmount the virtual floppy.
6) Use a program like Roxio or Nero (I'm sure a few others as well) to create a bootable CD. Use the virtual floppy image you created as the boot image.
7) Burn your CD.
Start your computer using the CD. It'll act like a floppy and allow you to start the BIOS flash utility. You won't be able to back up your current BIOS this way, since the back up can't be written to the CD...