Don't worry, if you would use inductive coupling to power your screen, you would still pay for the electricity. You would even pay more, are the link yield is quite poor.
Using higher frequencies may give access to larger distances, but the amount of energy that is transmitted is very low ! Telecom system only transmit information, often buried into noise... no row energy that you can reuse as such (unless you consider that information is energy, but that's another question).
You can see how passive tags work: distance is very low, and I can tell you the chips in the tags are extremely low power (a few 10-100uW usually). You can imagine that such an energy is not sufficient for a screen, even passive.
Therefore I suggested the solar cells. As long as I know, there are no other small energy sources available now.