The Carousel server itself may or may not be configured with a valid DNS server and should be able to function normally.
BrightSign Players before Carousel 7.4
When a BrightSign player makes any network requests to the Carousel server, the Carousel server will do a reverse DNS lookup on that player. If the server does not have a valid/reachable DNS server configured, the server will timeout on the reverse DNS lookup. This will cause all of the network requests from BrightSign players to fail.
The solution in this case is to remove the unreachable DNS server from the setup of your Carousel server.
BrightSign Players with Carousel 7.4 and later
When a BrightSign player makes a network request to the Carousel server, it still attempts to do a reverse DNS lookup for that player. If the DNS lookup fails because of a timeout, the Carousel server will no longer attempt to do a DNS lookup until the service has been restarted.
This will manifest on the BrightSign by the first network request failing due to time out. Following the initial failure, all subsequent network requests will successfully complete for all BrightSign players allowing them to function normally.