So type the correct name. Don't forget the instance name, if it is a named instance.
You say that you are on a different network, so the server you are trying to connect to may not be accessible. You say that the application connects, but maybe it is connecting to a different server.
And that is about all I can say, since I don't know anything about your environment. You may have to talk to your admin to find out how things are set up.