i think the idea is not to glue a rod onto the screw, but to set the superglue into a screw shape - so it can be screwed out with a flathead screwdriver etc. that way there are turning forces pressing against flat set glue, rather than relying purely on how well the glue has stuck to the screwdriver.

so you don't want a rod that fits the shape of the stripped hole, but a normal shaped screwdriver (flathead or philips or whatever, probably don't waste a triwing on this). that's what i think anyway

I would try cyanacrylate based super glue (which sets really fast) together with something that is as best the negative shape of the hole that's left, as can be. if you have some metal rod or old screw driver try filing it down to fit in the hole well before applying the glue. hold it still while the glue hardens, which shouldn't take more than 10 or 20 seconds.

In the worst of cases you can VERY CAREFULLY cut a slot on the head with a dremel disc or similar, but you must be cautious, and once you get it out, throw the screw out and replace it or just leave the hole...

I'd rather try the hot glue or some loctite on an old screwdriver.

Another thing I have tried which might not work in the confines of the gameboy battery compartment, is dropping a dab of hot glue or superglue into the stripped screw head then immediately holding the screwdriver head in the hole, pressing down hard and waiting for the glue to set then turning it.

I tried the rubber band thing and it didn't work. There is nothing left on the screw to catch on. I may try kitsch's stripped-screw extractor idea latter this week and Alley Beach's pen idea aswell.

Take a small, thin rubber band and place it over the screw head. It'll work 90% of the time.

i use a plastic pen. take out the ink/tube and melt the tip of the pen. then shove it on top of the screw and let it SET. then twist i took apart a few cart screws this way

try pliers, pinch real tight, and see if you can get it out this way

companies make stripped-screw extractors though.  i've got a set made by Craftsman (Sears brand), they work really well.  two part process, you drill out the top of the screw a little bit, then another bit goes backwards, bites into it, and unscrews the thing.

I recently got a DMG and one of the screws were stripped down to nothing and i can't remove it.
It's the one in the battery area on the left side.