Make sure your using the HTML5 player, looking at your first site it does not appear to be the new player. To activate the embed feature go to settings, media appearance and be sure to activate the embed link option.. So far as the player showing up, make sure you have set the default width and height in the settings so it fits in your posting area.
One way to make sure it is not the theme change your them to the default wordpress theme on a temporary basis, if the player appears as it should then their is a issue within your template if it still does not show deactivate plugins one at a time and refresh the page and see if deactivating any plugins makes a difference. The players were tested in a wide variety of templates and we know it works fine in the default wordpress template, this will help you narrow down if their is a plugin or template issue that we can then investigate.
If you view this page
http://www.powerpresspodcast.com you will see what the html5 player looks like in different browsers.