Only part one part of the model is being rendered I’m trying to do is a very simple animation: a mesh, a moving 3D–animation of a mouth. It has two layers: one is the lips (red), the other is the inside of the mouth which is black. Consequently I have 2 materials under the material slot. Under the mesh slot, I’ve connected the two parts of the mouth as a vertex group. I’ve created 2 shape keys: one for closed and one for open. These values are keyframed and will eventually be baked to a sound file, making the mouth move in sync. Everything looks fine and dandy when I play the animation. But when I tried to render it, all my previous problems seem very light indeed. First I couldn’t render anything at all. Finally I found a post saying and should uncheck the compositing and the sequencer. That made the trick. Almost. Problem is, it only renders the red part of the image. Can someone please help me out. Please?

I'm attaching one image, it seems that it is the limit here? I can supply more if needed
All what you need to do is move black part a little bit higher, because you have two faces on exact same level - overlaped. Blender can't know which one is on top.

Anyway: I recommend you search for some tutorials about topology and animations.