You could get something like the Niles CS12V...

http://www.ebay.com/itm/Niles-CS12V-Switching-Systems-/282346359492?hash=item41bd278ac4:g:nIMAAOSwiONYNhfh

But, I would just get a good universal remote control and use it to control the screen as long as your screen has infrared control of it.

You may also have an A/V receiver which has 12v outputs.

Or, you may have a cable box which has a switched output on the back you can plug a 12v power supply into.

There are many ways to do this if you want it to be automatic.