All machines, including the domain server and file server need to have DNS set to and only to a DNS server that is in the domain. There *MUST* not be any other DNS servers in the DNS list on any of thoses machines while they are in your network. As for WINS, it is best to install the WINS server on the 2003 server and let it handle being the domain master. Authentication is a 2 way street. The client is going to try and connect to the file server and the file server is going to try and authenticate to the D/C for the incoming connection. Both machines need to be able to talk to the domain controller. DNS and WINS configurations can be handed out by DHCP.
All outside DNS should be handled by the DNS server on the domain controller. That error is a DNS error that typically happens when someone thinks it is "best" to have outside internet DNS in the DNS list of the clients.
Verify you have a machine account on the file server and that the file server has successfully joined the domain.
Do an ipconfig /all on the DC, file server, and a random client that is having issues.
Ignoring the fact that I don't have a domain at home...
IP Address. . . . . . . . . . . . : 192.168.1.101
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Default Gateway . . . . . . . . . : 192.168.1.1
DHCP Server . . . . . . . . . . . : 192.168.1.1
DNS Servers . . . . . . . . . . . : 4.2.2.1
4.2.2.2
4.2.2.3
DHCP, default gateway, subnet, and DNS (in most cases) should be identical on all machines. I am assuming you are not doing multi-site networks with WAN connections however...
Another thing to look for, make sure you do not have a DNS zone of "." While not likely to be the cause of the issue it might be a symptom of someone entering internet DNS servers in workstations to try and get to the web. "." makes Windows DNS become a root server, 99.99999% of the time, you don't want that.