$post -> ID outside the loop. The result was I couldn't grab the data I needed to present subpages.
After more searching, I deduced the conflict was related to the <?php head() ?> equation. Once I eliminated that, I discovered the above equation would work. So, I have had to take down the sponsor slideshow widget for now.
Strangely, the conflict existed for anyone not loggedin as an admin. Maybe that will help track down the problem, as I really liked the widget :-)