The first thing to check would be to make sure that the two servers can still talk to each other. From the console of the first server see if you can ping the second server. If you can then see if you can telnet to port 1433 on that server. If you can check the DSN and make sure that it has the servers name and not an IP Address. Also check the client network utilities and make sure that there is no alias setup pointing to the old servers IP address.
Can you use Query Analyzer from the console of the SQL 2000 machine to log directly into the SQL 2005 server?