This a problem that, thankfully, I did not have to solve, as it was solved for me by others: my lone remaining Windows 98 machine lots its connectivity to my recently upgraded Linux Samba server.

The solution and explanation provided by Steve Litt is excellent, and I won't repeat it here. The gist of the story is that newer versions of Samba no longer have LanMan authentication enabled by default. The essential steps needed to get things working again are

1. Add these three lines to the [globals] section of your smb.conf:
   lanman auth = Yes
   client lanman auth = Yes
   client plaintext auth = Yes
2. Restart the Samba server;
3. Re input passwords for every Win9x user:
   smbpasswd -a username
4. Have every Win9x user log out and then log in again.