thats alot of trouble. setting up a simple motor with switch activation or program activation isnt fun.
can be done but big possibility of the motors burning out quick, you gotta set up a curcuit for when the motor stops, other wise youll end up with a burnt out motor in no time or stripped gears.
youll have to set up some resistors to keep from overloading the motors and probably a gear system as well. Try getting a book on robitic curcuitry, it will give you examples of gears, ratios, resistance levels, and if nothing else you got a good book of curcuits that you could have fun with and play with.
Only way i know of the pain is from highschool robotics.
I would say set up some string through a pully system sending them to one motor and allow the screen to fold down instead of pushing it up, reduces the strain on the motor scince youll only have stess on the motor going one way and youll have fewer moving parts. Youll still need to set up the timer cuircut or a tension curcuit for it to cut off so the screen wont go to far down and the motor wont still be pulling on the screen when its in place.
But it would be bad a$$ if you got it working w/o flaws. let us know how it works out.
If you need help, shoot a message twards me ill see what i can do to help.