It looks like I finally found the correct solution to the offline files problem. A couple of key facts that led me to the correct solution were:

1. “Make available offline” option is greyed out.
2. Folder remains read only despite efforts to change it.
3. When I tried to delete the folder, the computer said I should not delete a system file.

For a long time I could not figure out why the computer thought that the folder was a system file. Then I figured it out. I had redirected the “My Documents” folder to the network shared folder. I reset the “My Documents” to the default folder on the PC and deleted the files from the Folder Options menu. I setup the Quickbooks company file as an offline file. Finally I have only one file I am going to synchronize.