The EXACT same thing just happened to me. I tried all the other recommendations and none of them worked. This is what I did:
1. Ran a scan disk on my floppy. (Right-click on drive A, Properties, Tools). That took a while. While it did not appear to solve much, IT ALLOWED ME TO MOVE THE SPREADSHEET TO MY DESKTOP!! (simply click and drag)
2. Opened Word. Went to Insert menu and clicked File (Insert File). I selected my spreadsheet. At this point you have the option to select the entire workbook or each spreadsheet one by one. I chose the latter option, since you will see, one of the spreadsheets will refuse to copy - the BAD ONE.
3. Selected the first spreadsheet, hit OK. It got copied as a table in my Word document. I repeated steps 2-3 for all the spreadsheets.
4. Save the Word doc.
5. In the Word doc, click inside the first table, go to Table, Select, Table. The table is now selected. Right click, Copy.
6. Open Excel and click inside the first cell of the first spreadsheet (you will have to insert new spreadsheets as you go). Right-click, Paste. The first spreadsheet is now re-created in Excel. Repeat steps 5-6 for each spreadsheet.
7. Clean up your spreadsheets. This may appear tedious, but after you do it once, you can tell what all needs to be formatted and you will be able to do it all at once for the rest of them (usually, Format, Cells, Unclick Wrap Text, Rows/Colums Autofit and maybe click on the "align" buttons in the Property Bar). Also, some formulas may be gone, but at least the numbers ARE THERE.
I think all this is a small price to pay considering the alternative. Make sure you save a copy somewhere else. This was not caused by a bad diskette or a bad drive, it's rather a problem caused by Excel, so no matter what other media you use, it may happen again, so better safe than sorry.