2003 dns?

I am experiencing some issues on a small 2003 network with 2000pro clients. I can ping by host name, but get an “Unknown Host” repsonse when attempting to ping by full dns names. I am also having difficulty adding a global account to a local group on the clients. I can select a domain account on the local machine, but when I hit apply I get the following error. “Processing of object failed with the following error The specified domain either does not exist or could not be contacted” The clients are members of the domain. I am also unable to manage the client machines from the server. Any ideas?