What could be used on an island to make it self sufficient?

You do realize that there are actually people living in island nations that sustain themselves without electricity in this day and age. Towns and villages thrived without modern equipment too. I seem to remember reading about entire empires that dominated most of Europe, Asia, Africa, and the Middle East that did quite well without electricity so do you believe that this would be one of the main concerns of the few remaining survivors from a zombie takeover? I only ask because anyone caught in a survival situation won't be worrying about electricity as a priority. Water, shelter, food, and companionship are all basic needs, your ipod isn't. Sorry, I am a realist but I guess your novel is about zombies so realism isn't the focus. I would aim for a more primative living scenario using water wheels and windmills for things like irrigation and milling. Maybe eventually infrastructer and electricity would emerge but the transition from modern life to island isolation will be much more believable if you focus on the basics of human perseverence. I can imagine people sailing to the mainland (risking being eaten) to gather critical items like medications, basic tools, or maybe radios and batteries for communication but not to gather miles of wiring and computer components. Plus what the heck is going to be on the tube anyway, are the zombies going to start broadcasting the "Zombie Jersey Shore?" Just my two cents. Good luck with the story.