I've finally managed to get working WiFi on the old laptop I mentioned on here some years back! I found an old Linksys PCMCIA card and tried that and it worked! I'd post the spec of it, but pccardctl claims it doesn't exist, despite it quite clearly working and lspcmcia only specifies the sockets. Tinycore version is 6.something, kernel is 3.16.6-tinycore.
If someone can give me some alternative commands to get info I'll post whatever I can find out.