This is a longshot but are you plugging the USB drive directly into the computer or are you using a hub? If a hub, is it a powered hub? Some USB devices won't work with a non-powered hub.
I fully understand your need for a floppy drive. I also have hundreds of floppy disks around. I have both 5.25" and 3.5" floppies, boxes of them. I have a dedicated machine setup with both 5.25" and 3.5" drives so that I can copy data to/from my floppies. I also collect vintage computers and some of them are floppy only.
Once you get your floppy drive working, you should look into an app called WinImage
. It's an app that will allow you to make images of those old floppies for archival purposes.