So your HDD may be failing if debian is chugging at the desktop.

Try swapping it out with a cheap SSD.

~~Aside from Debian, you could experiment with the 32bit version of mint.~~

If you want a GUI, Puppy Linux is for you:
https://puppylinux-woof-ce.github.io/

I've got MX on a old EeePc and never had a problem.

Have a try with BunsenLabs

That's not a potato, that's a fossil.

Arch with LXQT, maybe? Then you can choose to install specifically what you want with minimal overhead. Another option is the minimal version of NixOS, but like Arch, you'd need to install a DE separately, and you'd need to learn how to use Nix.

But if it's still struggling, might be best as an art piece or command line only, given that a Raspberry Pi 4 and 5 can be had for <$100 and neither struggles with lighter DEs or browsers.

Q4os with Trinity desktop really needs little RAM and runs fast even on old devices. The desktop is a bit old-fashioned, but ok. You may also try lighter browsers, perhaps Palemoon.

But 4GB is actually not that little, almost all distros can run well with it, especially rather slim ones like Debian lxqt. maybe it's really due to the hdd.

Is gaming the main use case? If so, I think the distro won't be the biggest performance factor.

If gaming is not the case, I would ask myself this question: Is a desktop environment a must? Because you'd be surprised by how much you're still able to do without one.

You can try Void. With 4 Gb it should be a breeze. I'm rocking it on a netbook with an atom processor and 2 GB of ram and I use Firefox on it without any issues.

Mmm Sandy Bridge or at least I hope so or that is closer to a 20 year old potato.

Mabox!

you can always try a puppy distro! they're super barebones and you can get them really lightweight, shouldn't really have any problems with running something like one of the slackware-based pups or maybe an older debian pup. you can check it out here! https://forum.puppylinux.com/puppy-linux-collection

I had a net top thing from asus that had worse specs than that running fine a few years ago on AntiX. It was just used as a thin client mostly but did the job.

Let us know what you go with!

Debian can still work, but you'd have better chances with legacy LXDE, or starting with no DE and installing IceWM.

Q4OS Trinity, antiX, and Damn Small Linux are all Debian derivatives known for being able to run on very old systems, and they're among the most lightweight distros I know that are still functional for most purposes.

Antix