This is so cool, what are some great uses for this?
Granted, this is pushing it, but I've been using this setup every day for almost two years. (I just like to use old hardware until it dies -- or, is this what old IPS-screened Thinkpads generally turn people into?)
Sure, you probably should be a "computational minimalist" by nature (e.g. there is an older version of Chromium, but I suppose your main browser will be Dillo -- which, actually, is just wonderful once you get used to it). But if you are a minimalist, I'd say it's a really solid system.
Also, it's fun for me to think that I bought this Thinkpad T42 three years ago for €20. And now I use it as my main workhorse in a field where typical setups consist of new-ish MacBooks with high-end SSDs and an up to date version of Pro Tools. (And where people occasionally still think that "duh, you can probably only edit a text file in Linux".)
So it's an awesome, clean, fairly easy to maintain distro (e.g. in case of a typical install you have a pristine system after every reboot). And the community is very friendly and responsive.
Nowadays I've found myself mostly using it for VNC to a slightly better machine (my old desktop, on permanent loan to a family member after their laptop broke. This works...). And... even on my not-great 802.11g, and the CPU even locked to 800MHz, typing this text over TigerVNC is literally realtime with no perceptible lag or delay. I'm honestly amazed. But anyway...
FWIW, launchpad.net have multiple sources providing the latest 32-bit builds of Chromium. These are built for Ubuntu, but I find they've worked 100% fine on Slackware. :P (After some work I even got the debugging symbols into the right place!)
(Nothing stopping you from building the world's largest LD_PRELOAD to pull in "enough Ubuntu" that Chromium boots, but I find that 100% unnecessary at this point.)
Some build daily(ish), some build fortnightly-to-monthly-ish. Before I set up VNC, I was in the process of figuring out an autoupdate script (CLI PHP, easily rewritten) that would find and fetch the packages off Launchpad. Let me know if you'd like a copy, I never finished it but I did do the Herculean bit of figuring out the magic API URLs, the rest is just boring scripting and downloading.
Protip. If you open 100-170 tabs (possible! on 2GB! with The Great Suspender), the main process will hit 4G VIRT. xD
Besides that, NetSurf is a bit better than Dillo, you're probably already aware of it.