Windows 2000 Server is *comletely* different from NT 4.0 Server.
Authentication:
First of all if you configured this machine to be a domain controller, it will NOT participate in domain security with the NT4 servers (hence the reason it asks forauthentication every time you try to connect to it). You must either demote your NT4 PDC's to BDC's, or configure the 2000 server as a peer, and not a domain controller. (If you demote your NT4 PDC, you must configure 2000 for mixed-mode.)
Server not visible:
Because of authentication (or lack thereof), this server may not be visible because it's machine account in the domain would not be valid. Unlike NT4, Windows 2000 does not use WINS for name resolution by default. You must manuallyinstall WINS from the Add/Remove Programs control panel.
Refused Connections:
You're on your own there. I can't think of any reason other than you simply didn't specify enough licenses during setup. If this is an Eval copy, there is no way to increase the license count.