In any real apocalypse situation...
There is only one real use for any computing device that I could justify the luxury of generating electricity for. That is knowledge preservation, and there are far more reliable, low tech, time tested methods for doing that. The only real benefit of the computer form factor, and I would be using a tablet or at most a laptop, would be the sheer volume of reference material you can store one any modern computing device. Pair a tablet with a sizable number of SD cards and/or USB sticks and a portable solar charging unit and you can set yourself up quite comfortably once you find a safe place to settle down and farm sufficient food to survive long term.
Otherwise there will be no internet as people will be far more concerned with survival than keeping power and telecom systems up and running so most of the paranoia induced arguments for open source to oppose evil corporate influences become invalid.
