If you were doing an animation, you could probably make a gaussian blurred low-res version of whatever's on the screen and use that as an animated light gel. (Assuming you're using an animated texture on the screen here.) Then the bright and dark changes of whatever is playing on the screen should follow through in the light it casts. (Other ways would need manual keyframing, wouldn't they?) Still shift it blue a bit, since most screens seem to have that shift in their color temperature.

I might have to try that sometime...

---

Barbequed Pixels?

Your friendly neighborhood Wings3D nut.
Also feel free to browse my freebies at ShareCG.
There might be something worth downloading.