I just realized the semi-stupidity of my question. I should have said "modern web", considering the ARPANET could be considered a type of "internet" (?) that ran using hardware from 1969? Thank you for the replies though, something to read up on.
Even that leaves a lot of room. If you can fix certificate problems, any simple browser (even text mode lynx) can still do a lot these days. But let's go really "modern", i.e. being able to access web applications without missing features, timeouts etc. Slower, maybe just one at a time, but what you do works. That's surprisingly hard. I sometimes use TenFourFox, a browser for Power Macs, which is a bit of a mashup be…
a. 2gb of ram as my raspberry pi with 1gb ram cannot handle more than 4 tabs in chromium responsively.
b. ssd, connecting to SATA, it makes my 10-year-old thinkpad feels new.
c. enough cpu power to handle 2mb of js
d. hdmi connector
That limits the choices to computers not older than 15 years old, plus minus several years.