I got same problem too, I already read this topic over and over again hoping that anybody have the solution. Problem like <Workgroup Name> is not accessible.....but can access the shares on other computer by mapping drives. Until, when trying to figure out why, I noticed that Computer Browser in the Services is Automatic in the StartUp Type, but it is not running, 5 of my computers have same situation. I try to run the service, restart the computer but end up same situation. So I click on the Recovery Tab of Computer Browser Service & in the failure, I choose Restart Service instead of Take No Action. I re-run the the Network Configuration Wizard, reboot, disable the firewall....and everything is fine now. I've run this procedure on all of my 6 workstation,,,,Now....everything is fine I can now browse my Network with my Network Places, View Workgroup Computers....
If you can browse the computers but cannot access the shares/directory on it, try the procedure of SirGawain http://www.thetechguide.com/forum/index.php?showtopic=9932&st=20
this works well....
I'm running Windows XP SP2 on 6 workstations....