New DNS having trouble

Well I'm new to all of this but i'm working on the computers from my work and they recently obtained a new DNS as well as IP numbers for the server and computers. Now my issue seems to be that I have the new DNS number and I put it into the server computers as well as putting in the IP adress since it's all static. But as son as I put them in the internet goes down and no one can log in to the network and the remote users can't seem to sign in either. Is their something I'm doing wrong??? Or if someone can walk me through the steps of how to change the old DNS to a new one so that all the network computers can function that would be helpful. Thanks