DNS Trouble

My Windows 2000 server is the only DC in the private Domain and acts as DHCP and DNS server with AD. Attached is a CISCO 770 ISDN Router. Name resolution in the intranet works fine but not so for the internet. When I ping the ISPs DNS server a connection is established immediately. As long as this ‘Pinged connection’ stays I can do IE and e-mail without any problems. Trying to establish a connection to the internet by opening IE or Outlook doesnn’t work..
So this seems to be that the physical part is fine. The router is fine but something with the ‘forwarding’ to the router is not working. Any ideas? Your hints are very welcome !
Wolf G.