internet and server 2003 and network DNS issue

Hi,

We have a server 2003 office domain. It connects to the internet via a sonicwall router then out to Charter on a static IP. The gateway is a static IP. When our server with Ad that controls all users is up, we have internet, and when it is down we don't. But, the gateway is set in all workstations, so we are trying to figure out why a workstation can't get out to the internet even when our server is down?

Thanks!