I've had luck wetting the media inside the floppy with isopropyl alcohol and either spinning it by hand for a bit or running it in the drive, of course it doesn't always work but it could be worth a shot. Sometimes if you look a the disk through the window you can see where the problem is and clean it with an alcohol-soaked cotton swab.
As for downloading it and rewriting the floppy, as a last resort and after determining the disk is still usable (good luck there) I cant imagine anything wrong with that.