Let's start with the basics:
Turn off any firewalls for debugging. If the firewall is the problem, you'll have to configure it to allow access to "trusted zone" addresses. Note that some firewalls must be completely uninstalled to stop them from affecting your networking.
PING each computer by IP address, and if successful, PING by name. You can obtain the IP address of a computer by opening a command prompt (DOS window) and typing IPCONFIG. This should work for any Windows version.
All computers should be in the same workgroup for computer browsing to function properly. File & Print Sharing has to be enabled on any computer you wish to share files or printers from. You also need to actually share the resource in question from My Computer, right click on the drive/printer/folder, and select sharing.
If you encounter difficulties accessing computers that are visible in Network Neighborhood, make sure the computer being accessed has an account with the same name/password as the system connecting to it uses to login.
While the default NetBIOS setting is correct for normal network configurations, it's possible for it to be altered, and it costs nothing to make sure it's correct. NETBIOS over TCP/IP must be enabled for normal network browsing.