Terry,

This can happen if you recently saved a file to floppy disk and there is a
shortcut to this file in the Recent Documents folder (on a single user
system this is C:\Window\Recent).  If so delete the shortcut. Other things
you might wish to check include:
a) Motherboard bios.  You might want to change the boot order to Hard Disk
rather than what may well be i) Floppy, ii) CD-ROM, iii) Hard Disk
although if you do this you will need to change it back if you at some
later date wish to boot from either a floppy or CD.
b) System Properties | Performance | File System | Floppy Disk.  Uncheck
if checked "Search for new floppy disk each time your computer starts".

"Start, Settings, Taskbar, Advanced...>click on Clear for items that may be
in the Recently Accessed Programs
and Documents".   I'm not using Me anymore, so, this is sketchy at best.   I
think you can also right click a vacant area of the Taskbar, select
Properties and on the second tab, I think there is an option to clear
recently used documents and programs.... roughly the same thing as before.

Also, there is an option in the BIOS to seek the A:\ (or floppy) during
boot, enabling you to boot from a floppy disk.  If this is something you do
not desire, it will have to be disabled in the BIOS boot sequence.  This
option enabled should not cause the floppy seek for applications, of
course....only a check for a bootable disk during bootup.

Try the above, if that does not resolve the issue, post back.   Win Me
maintains a "list" of recently accessed items, one of which may have been in
your A:\ drive.
                                   Heirloom, old and oughta work