When testing the connectivity to a DNS server, due to firewalling, you can't fully trust ping (ICMP ECHO). Instead, ask the name server in question to look up it's own name by address. If the name server and the net between it and you work at all, this basic request will go thru, and will look totally innocuous in case the admin on the other side is excessively paranoid.
The UNIX command to do this is
$ dig @IPADDRESS -x IPADDRESS