As you haven't provided a chef server version or any platform specific details, I am going to take a stab at this.
If the IP and DNS name has changed on the restored server, it could be one of the following:
- Incorrect DNS name configured for the SSL cert for the Chef server (This would prevent Chef from loading correctly)
- Incorrect SSL certificate on the client/nodes for the server (Authentication issue at the end of the day)
- The nodes
client.rb file has the incorrect Chef server URL
At the very least I would start there.