On my website at http://billthelibrarian.com, I have one set of Parent and Child pages. The child pages are not displaying as a drop down at all. It is white menu bar under my logo, the very last one labeled "My Book." I am using custom menus, the latest version of WP and the latest version of Atahualpa. Any suggestions? I have tested it in IE and Chrome browsers.

Did you apply the patches for 3.6.7 as outlined in the new versions and updating forum? That may do the trick for you. You should apply them all as they will all be incorporated in the next version.