Instead of using the Browse button, try typing in [Domain name] \ [username] and then the password. Are you getting anywhere? Do you know which server is the Domain Controller for this domain? Do you know its name or IP address? If you do, could you go to Start > Run > type in ping [Domain Controller IP or name]? If you do this, what ping replies do you get (do you get Request timeout?).
What you should also do, is go to Start > Control Panel > Network Connections. There, right-click on your network connection (i.e. Local Area Connection) and go to Status. There click the Details button and see the following:
Default Gateway address
DHCP server address
DNS server addresses
Try pinging all of them and see if you're getting replies. If you do - then, as squillman says, the computer is not connected to the domain, thus you can't access its user lists. If you don't get a ping to one of them, problem is somewhere else.