The old TRS-80 Model 100 fits some of the goals. It runs for a long time on just four AA batteries. But it's text only and perhaps even too limited even for 100R. I'd love to see a modern version of that machine with a bitmapped display, running a minimal (not Linux) OS, that can run for months on four AA batteries. Maybe something like a somewhat upgraded Psion 5. I think much of the Psion software is available so maybe it's actually a possibility.