There are two likely scenarios here
1) The name of the router does not have an “A” record in the DNS
2) The NT machine which serves as your DNS server is not using itself as a DNS server – check your TCP/IP configuration. Note: Just because a given machine (of any O/S) is running DNS does not mean that the machine automatically uses itself for that purpose.
3) The NT machine does not have the default search domain set to whatever is local or configured for the name of the router.