Cleaning out the basement, I came across a Dell Latitude XP 4100CX: a 486/100 with 24 Mb RAM and 500 Mb HDD, and a tiny color screen. Hard as it is to believe, Linux will run on this, too. Found instructions on how to proceed without a CD-ROM drive here: http://www.damnsmalllinux.org/network-install.html
Remarkable.