That particular room has three exits, but the exit with the battery requires you unlock the Super Magnet for east magnetism. Now that the jam is over, I've uploaded an updated version of the game with a comprehensive map that should make exploring more fun and less confusing so its easier to find where you need to be going. Also touched up on a ton of stuff, art, sound design, etc. If you ever decide to give it another try, it should be a bit more intuitive and accessible this time :)