Open the mail activity window available within Mail, and see if this gets busy with something. Mail can sometimes get confused, and try to re-download stuff.
DNS translation errors can cause a ~30 second delay in all network activity. There’ll be almost no network activity, and a DNS translation error—as opposed to a DNS server error that can fail over to a second DNS server, there’s a reason most folks have two DNS servers listed—will effectively block all access as the IP address of the remote server cannot be resolved. There’s no identified server available to connect to.
DNS errors will delay or will prevent all network activity, other than the (rare) cases where a remote IP address is already known, or when there’s some other means to identify the remote server, such as Bonjour-based connections on a local network.