The Win98 machine that couldn't see any of the local machines on my network but could somehow get packets through my gateway to the internet despite not being able to ping (or respond to pings from) the gateway ... is now working correctly.
Details sometime after a) I figure out the Samba problem I'm having -- one I've solved before but long enough ago to have forgotten how -- b) possibly had a nap, and c) probably been to Bowie and back. For now I just wanted to share the news that it's working.
[UPDATE: Details posted.]