You are looking in the wrong place for a solution.
The computers you see in Network Places are simply the computers that are returned by the Browse Master when it is asked to report its network list. An empty or non-existent Browse Master is almost always caused by a misconfigured firewall on even one of the machines connected to the subnet. Firewalls interfere with Browse Master Elections and on network startup, more than one computer becomes browse master. Things work for a while until the real browse master gets tired of receiving announcements from the firewalled computer that the firewalled computer is a browse master and then the real browse master quits, relinquishing control to the firewalled computer which is non-functional because of the firewall.
"Internet firewalls can prevent browsing and file sharing"
<http://support.microsoft.com/kb/298804 >
Sometimes you can find the offending computer by searching the System Event Logs (Start -> Run -> "eventvwr.msc") for a warning or error that reads something like: "Computer xxx claims that it is Browse Master. The browse master on this computer is stopping". This would point to computer xxx as your problem.
HTH,
JW