CiviCRM select box items can't be selected in wordpress page create
I had a similar problem with this - See CRM 18496.  It turned out that there may have been interference with CiviCRM's jQuery and CSS from a Wordpress plugin.  You could try deactivating any plugins that you have installed, one by one, to see if there is conflict.  My problem went away without me discovering which of the many plugins I have was the culprit but one of them that I deactivated was Jetpack.

Unfortunately, you can't test this out on the demo site because you can't there create a new page in which to enter the appropriate civicrm shortcode.