I think a laptop would work with the bottom half (Where there is currently a keyboard + trackpad), as a second LCD which is touch sensitive.

The default arangement could be to simply have a keyboard displayed on the bottom half, with a trackpad area, but then with other apps you might want to manipulate graphics, or paint, or do other cool stuff on that bottom area.

It'd take a little while to get used to non moving keys, but typing on the iPhone is pretty easy once you get the hang of it, and I'm sure there are technologies that could give some sort of little feedback to the fingers.

(This sounds quite like an enlarged Nintendo DS really).

That way also, you get one clean LCD, and a separate one that gets a little dirty from fingers, and has to be cleaned. Seems a good plan to me.