Anything I can do about that, or just write it off?
Don't write it off yet.
Have you any spare floppy discs? If yes, format one of them on your new machine. Then, find a friend, work colleague or anyone that has a machine with a floppy drive on it, and first make sure that the "new" disc reads OK. Then, try reading the old disc. If it reads, "borrow" some space on the machine you are at and save the files there, then put the "new" disc in and save the files to it. As the new disc was formatted on your machine, it should read OK when you get it home.
Floppy drives are not quite as compatible as some manufacturers would like us to believe, so it could well be that your original disc is not stuffed, but just can't be read on the new drive.
Then again, it could be the case that this won't work, depending on the settings of the drives concerned.
Another option would be try the "old" disc in a number of machines, if you find one that works, "persuade" the owner to send the files via E-mail to your machine.