An external floppy usually connects via USB. In order to boot from a USB device, you will need to have a fairly modern motherboard that is capable of booting from a USB device. In other words, it needs to have USB drivers contained within its BIOS.
I am puzzled by your description of your problem.
What version of Windows are you using?
If Windows recognises your floppy, but the BIOS does not (?), do you mean that you can read floppy disks once Windows has loaded, but not boot from the floppy drive?
Who has told you that the motherboard is at fault, and what explanation did they give?
More info, please :)