Considering how simple the model is, I think it'd be interesting if you tried to replicate the effect of the depth of the screen. I mean, cut out the screen portion from the model and then insert a single quad inside.
Err... this is hard to explain, so like this:

There is no shadow effect in place, I just used a very simple texture like so:

You may also be able to simplify it and extrude the screen into it, but I'm not sure if it would accurately replicate the effect.