Plato, putting words in the mouth of Socrates in Phaedrus wrote:
...for this discovery of yours [writing] will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves.
http://en.wikisource.org/wiki/Phaedrus#On_the_decline_of_Gre....
Chess players can play without the chess board.
Some writers prisonners wrote books in their head.
Similarly, if you were separated from your computer you could still write programs, in your head. You would have to be very carefull, but you could reach a stage where the program is debugged well enough that you could just type it out (once you've left out the the prison), and have it run on the first time.
Just avoid TV and its brainwashing (cf. Fahrenheit 451, http://www.laweekly.com/news/ray-bradbury-fahrenheit-451-mis... ).
Which while exaggerated a little in your version, is more or less what earlier programmers (without monitors or even terminals and with expensive test-runs) did. Of course they also used paper, but it's interesting how much of the program they could keep in their head.
Heck, even something like "ex" (the editor, which only showed the line you operate on), needs some of that capability to note stuff in your head to ever work.
My memory is bad because I rely a lot on technology and paper to remember things for me. One are I have improved is by learning Haskell using Vim and not having an IDE like I do for .NET I have found it has improved my memory. Also starting to learn another language has probably helped me.