You could use a decal to limited effect. Think WW2 fireplace + small fire decal, only what you need is a hollow TV model with a screen decal inside it. The limits are you'll only have 16 frames and they'll play at a fixed (and fairly rapid) pace.
There might be some mileage in the animated model idea though... I'll have to give it a try. I've been looking at ways to do display screens, using particleIllusion SE to create the animation frames, but they run way too fast as decals. If I put half a dozen of them on one wall the player would probably have a seizure looking at them