The actual problem has nothing to do with disk space. Excel is trying to display a security warning about the file you want to open, but for some reason it is unable to. Security warnings typically come for files you downloaded from the Internet, but not always. To work around this problem, you need to answer the security prompt before Microsoft Excel tries to display it. This seems to be caused by a compatibility issue created by running older excel file versions within excel 2016.
This works better if you usually store your downloaded Excel files in one folder. In Excel, click File » Options » Trust Center » Trust Center Settings » Trusted Locations. Click Add new location. Browse to the folder where you store your Excel files, select Subfolders of this location are also trusted, and click OK.
Any files you save to this location will be automatically considered trusted and therefore open automatically without security warning.