"why would I have to do mount and unmount?"
In the beginning Linux required the user to mount and umount mountable devices by hand. Fairly recently automount was written which allows the user to insert a floppy or CD into the machine without using mount commands. And when you pull a floppy or CD out of the machine automount sometimes notices and sometimes doesn't. Whether you use the manual mount or the automount is an install option and/or can be changed in /etc/fstab.
In reading your description of your floppy behavior I came the conclusion that you probably had automount in your first installation and have manual mount in your current installation. So try using mount and umount to diagnose whether you in fact now are running with manual mounting.
For what it is worth, I prefer manual mount because that way i do not get into disagreements with my computer about the mount status of my floppy or CD.
Be prepared. Create a LifeBoat CD.