Ahhh...OK.
Two things:
1. Do other devices show under Devices - i.e. external HDs, USB flash drives, commercial discs? It could be possible the the Devices are "hidden"
2. System Preferences > CDs & DVDs > When you insert a blank CD/DVD: Set to Open Finder. That should mount a blank disc on the Desktop, which would allow you to drag your files into and then burn.
C
Thanks again, Mr. Cooper. Re 1: Yes.
Re 2: Had done that previously. What I had not done was look on the Desktop. Following your instructions I did so. I the dragged and dropped the files into the blank disk icon on Desktop. This opened a new Finder window in which the Untitled DVD was still misplaced. However, as an experiment, I dragged and dropped the files from the Desktop Icon to this new Finder Window. Things looked pretty much as before, so I then ejected the disc. Then something new happened, I was presented with the opportunity to burn the 'Untitled DVD'. I did so. It took awhile, but when finished, the Icon immediately vanished from the Favorites and reappeared under Devices. The files are now on the disc (I checked by using another machine). Also, now when I insert it, it appears as a Device, Only the unformatted discs appear as 'Favorites.'
So, once again, Mr Cooper, I am very much indebted to you and ever so appreciative of your kind generosity.
Now, I think there is some way for me to mark this Thread as Solved, I'll try to figure out how.