I am guessing over 48 hours.
PSP slim with 2200mAh - 8 hours (low brightness, volume 2 below max, 200mhz)
PSP fat with 2200mAh X 2 - 5 hours each (low brightness, volume 2 below max, 200mhz)
DS lite with stock battery - 5-6 hours
GBA (no afterburner) with internal 3600 rechargable lithium battery pack - 10 hours
Neo Geo Pocket - I forget how many batteries (I think 4), but Ni-Me, 3000mAh - over 8 hours
Virtual Boy with 6 3000mAh rechargable Ni-Me batteries - over 6 hours
Game Boy Origional - with 4 rechargable lithium batteries - over 6 hours
I also have extra 1800 and a 1200 batteries for the PSPs, and I generally keep 8 AA Ni-Me charged, so if we are allowed to use our extra batteries I could play a long, long time. I also have 2 UPS batteries. If I shut them off right away I could later use the 1 battery which can start up without AC power, run it for a few hours charging batteries and then just before it run out, I would jump start my other battery which can run for an hour or two if it was just powering things that are charging. I cannot live without power and never do.
Although I would probably just play my PSP slim in the event of a power outage, I could cycle 6 freshly charged li-ion batteries through it and play nearly forever.