If Excel fails to repair the workbook when you select the "Repair" option, open the file again using "Open and Repair," but this time select "Extract Data" instead.

Excel may not display the XLS file if another option is selected, giving you the impression that it can't open it.

If Excel Online is not working and you see errors Couldn't Open the Workbook, or Request Was Taking Too Long, then see this post for the fix.