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.
Swap in a new display controller board, get a cheap Bluetooth keyboard and wire the eee PC (maybe?) to the controller board. Then, remove the internal board and drive to make space for an old Android phone on which you can install a Linux distro.
Voila! A "laptop" that you can upgrade whenever you get a new phone or if someone donates a phone to you.
WireGuard, and an external HDD. Run at a remote location for off-site backup.
I do this with a raspberry pi 3 at the in-laws. I copied the data over locally before setting it up, and after that it's just nightly incremental rsync, which is fine even over my slow (35Mbps) upload.
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
Could you really? E-waste recycling is a great lie made so that people don't get remorse over throwing away their devices. Electronics are too complex, diverse and full of toxic stiff to be property recycled.
If anyone wants to dive more into this, there has been some projects where people from higher income countries put tracking devices inside e-waste before sending to "recycling", to find out where they end up. Spoiler: in poorer countries, to either be scattered around, thrown into a landfill, or be scavenged by underpaid people without any protection equipment.
Assuming it's not completely useless for this purpose, you could load FreeDOS on it and use it for playing older PC games.
MS-DOS 6.22 would be sub-optimal as it was designed with 486-era and older hardware in mind and since it doesn't support FAT32 and only supports FAT16, you're limited to 2GB partitions, while FreeDOS is actually designed with newer hardware like this in mind and supports FAT32 and thus larger drives.
Could use it kind of like an extra monitor with something like Barrier.
Could use it like a home assistant for a kitchen or something, but I don't know if there's any good privacy respecting software for that ATM (looks like MyCroft went bankrupt).
I used an old laptop I had laying around for controlling a Maslow CNC. Could also use a laptop to run OctoPrint or something.
If it has an ethernet port (or perhaps a USB to ethernet dongle), maybe a PiHole DNS using Debian or the like? It is apparently supported on other Linux distros than Raspbian.
If it supports micro SD XC (i.e. capacities higher than 32GB) or you have a USB hard drive or high capacity USB flash drive, maybe a samba server for file storage? I often use my file server as a substitute for digging out a flash drive any time I want to quickly pass a file between two machines in my house.