For a small number of different screen textures, you could use the Random output in the object info node to create a map to use dfferent textures for the screen material. Like this:
The huge disadvantage is, that you have to add each texture by hand and add another level to the mix RGB nodes with the masks.
I think a much better approach, especially for a lot of variaton would be to create a single texture with all the different screen images and use the random values (maybe based on the position of the object) to shift the texture to display different parts of the texture on each screen:
