I have a control that I am unable to access in the codebehind, and I believe it is because it is defined in a DataTempalte.
The overall control is a slide show carousel.
I would normally recommend not to touch UIElements from code... but the MediaElement is a special case... maybe you should wrap the whole template inside a usercontrol (maybe with some custom DepProps) and that will give you better control over the whole thing.
Edit: Another approach would be to create a Behavior with a couple of properties (such as IsPlaying) and manipulate the mediaelement from there. Then you could use this behavior in the XAML of the DataTemplate, with no need for code behind or usercontrols.