The problem MAY be with a .PIF file that points to the floppy drive. This file would point to the floppy operation in DOS, as opposed to the .LNK that points to it in Windows. If such a .PIF file is in either the Desktop or the C:\Windows\Start Menu folder, it could be causing you problems, and it doesn't need to be there for Windows purposes. If you find a .PIF file there relating to a floppy, move it to another directory (folder) and see if that will solve your problem.
Also, as Ray436 implied, the antivirus program may be set to automatically check the floppy drive. You should be able to disable that option in the program's "preferences," "options," or "settings" menu (depending on the software). Also, if you find an option there to check the floppy upon reboot, disable that, too. Hope one of these works for you.