I remember various old Pong type systems just running off of batteries, I'm sure they're pretty energy efficient.

Just add one of those floppy based cart backup units to that Genesis tower you've got going and you'd be set, bonus points if used with a parallel cable to a computer instead of just floppy disks. And of course nothing but glass CRTs for extra energy efficiency, double bonus if you run the sound through a stereo receiver instead of the built in TV speakers.