You should also give a bit more information about your set up. What Linux distribution are you using, and on what type of hardware. Is your floppy part of your computer, or is it a usb plug in floppy?
Fedora, for example, found that since the floppy is more or less obsolete, they removed it fro the initial boot. The problem was similar to your problem. If the floppy was empty, it might not mount correctly. I've seen the same problems with CDROM drives. The problem first arose during set up, when a line was put into fstab during installation. Removing the CDROM line from fstab cured the problem. I don't know if the same thing will work with your floppy problem, but, it's worth looking at /etc/fstab.
With Fedora, if I have a floppy in my computer, I first have to use modprobe ... example:
then I have to mount it:
Then again, if it's a usb floppy, it usually works without any intervention.
Are you confused yet? Well, lets first look at something.
Find the word Terminal in one of your menus (Usually the System Menu) and click on it.
Type "su" (without quotes) and hit return, then,
Type "cat /etc/fstab" (without quotes, and yes, there is a space after cat), then,
post that info here (copy & paste would make it easier)
Tell us what Distro your running, and maybe we can help some more.