What could I do with an old Toshiba Satellite A200?

With 1 GB of RAM, I'd start with a console-only setup or a lightweight window manager such as Openbox or IceWM. Tiny Core Linux is one option to investigate. Check that any system you choose supports the processor's 32-bit architecture before downloading it.

For browsing, Dillo or Links may be worth trying, but expect limitations on modern sites. A lightweight desktop won't make today's web pages lightweight.

Turn it into a small home network server. A console-only installation could serve files, family photos, a recipe collection, or a simple status page. Keep expectations modest and back up anything you don't want to lose.

Retro games seem like a fun fit. Try older PC games or lightweight emulators, though performance will depend on the game and emulator. Lakka is a retro gaming system worth investigating if a compatible build is available.

For old Windows games, an offline Windows XP setup is another possibility. The broken speakers mean you'll need another audio option if you want sound.

It's also okay to recycle it rather than spend money on upgrades. The old processor and hard drive will still limit what it can do, even with more RAM. If none of the small server or retro gaming uses appeal to you, recycling may be the better choice.