You bring up an excellent point, and one that often gets short shrift amongst the fray of strategies and tips. Simply put, staring at a screen for 4 hours fatigues most. Not sufficiently practicing on a computer screen can make test day even more stressful, as you pointed out. (Here is a helpful post that expands on this point:
Overcoming GMAT Test AnxietyThe good news is you are not alone. The even better news (don't worry no bad news here

, is that there are ways for you to improve your endurance for taking a CAT. Most notably, the GMATprep offers two on-line tests, which, since they created by GMAC itself, have the same granular, pixillated look of the actual GMAT CAT (not to mention the same deviously concocted questions

).
There are also other online tests out there, such as
MGMAT 6-tests. Taking a test once a week should definitely help you become more accustomed to the screen.
Another avenue for honing your CAT skills is
Magoosh. Our entire GMAT product is computer based. Indeed each questions comes with a clock, so you're not only getting the experience of solving questions on a computer screen, but are doing so under timed conditions. And our hours and hours of video lessons make learning in front of a computer almost second-nature

.
Hope that helps, and good luck!