Th problem has been found. HostGator updated the PHP because the previous version could not properly do all types of GIFs. All GIFs work now with the updated version.
Thank you for your response. There is only the HTTP error message within the media library when I attempt to add the GIF to it. I have discussed this with HostGator and we have not determined what is causing this problem, yet. Some GIFs work, but far too many do not.