Go into Element 3D. There will be texture maps, most likely, one for the body, one for the chrome bezel, and one for the screen. You can test which is which by turning the textures on and off, if they're not clearly labeled.
Create your animated texture for the screen and put it in the same comp. Make the texture available to Element 3D by listing it as a Custom Texture. Now apply that texture to replace the current one. If this isn't clear, the VideoCopilot site has tutorials specifically on this.
As for passing an object behind the E3D layer, you have to have the layer passing behind your E3D layer beneath it in the stack since E3D is applied to a 2D layer and doesn't interact with any other layer in the physical space. So short answer, pay attention to your layer stack.