In a WAN, the use of multiple segments without a WINS server breaks browsing so you must have NetBIOS name resolution for browsing to occur. In a Windows 2000 domain, DNS provides name resolution, but not for browsing. With only 32 computers, it is unlikely that this is the problem, but it is another thing that can prevent browsing from functioning.
It's also interesting that you have 33 systems on your network. Browsing typically sets up a master browser for every 32 systems --- perhaps this is part of the issue. While the browser service is not necessary for browsing to occur, the browsing service is used by the master browser. If all clients have the browsing service turned off, perhaps there is an issue here.
A good article on browsing issues and some information on tools used to trouble shoot them can be found in the transcript of a web cast at http://support.microsoft.com/default.aspx?scid=%2fservicedesks%2fwebcasts%2fen%2ftranscripts%2fwct061003.asp.
This was first published in February 2004