What are some fun or unconventional uses for an old Atom notebook with 2GB RAM?
It's not worth shipping and handling, it's beaten up, and I don't know anybody who wants it. Nothing is upgradeable, unless you count inserting a microSD card.
Of course I could use it as a janky media server or a dumb SSH terminal, but I've already got other machines for those jobs. Or I could recycle it, but what's the fun in that? Suggest me your wackiest programs to try, dangerous distros, or most unorthodox setups to make use of it.
I don't think there's any useful way to put it to regular use for yourself, but you could:
install debian on it and keep it around in case of an emergency. turn it on once in a while to keep it updated (doesn't need to be that often, it's debian)
use it on the go (no worries about it getting stolen)*
use it a place where you wouldn't use your main laptop as to not risk damange (camping, hiking, on a trip, etc)*
install a friendlier linux distro and give it away to someone who doesn't have a computer (a 10yo cousin maybe)
give it away to someone who has a computer, but doesn't have a second one and might be happy to get one to play with
*though i imagine the battery is not in good shape given your "beaten up" description
to play with, sure. but in the case of a backup machine, you want something reliable, rock-solid, low maintenance and easy to use, which is why I recommended debian