Problem SOLVED. --
Ongoto: I messed around and found that I could open a terminal window form the desktop as you described and, fortunately, since I had my internet connection previously setup, I was already logged onto the internet. However, I didn't reinstall the task-gnome package as you suggested. I initially started to, but noticed that a large number of dependencies were required that weren't on my machine. I concluded that if task-gnome was the missing package, then the dependencies should already be there. This lead me to keep looking. While searching the 'net I ran across a similar problem someone else had had and the recommendation was made to reinstall gnome-panel using; apt-get install --reinstall gnome-panel. I opened a terminal window on my desktop, logged in as root (su) and reinstalled gnome-panel using the apt-get command line above and then restarted my machine. Upon logging back in the panel was there!!! Life is better now.
Thanks for your help as it got me to looking and thinking.
p.s. gnome-panel is not listed by Synaptic as a separate package for installation. Consequently, the only way I could figure out how to fix the problem was to use the command line "apt-get".