Need DNS troubleshooting help with one domain

We have one domain that our server cannot connect to

; <<>> DiG 9.3.4-P1 <<>> boe.ca.gov
;; global options: printcmd
;; connection timed out; no servers could be reached

I can query some other servers and retrieve the information such as
$ dig @8.8.8.8 boe.ca.gov

; <<>> DiG 9.3.4-P1 <<>> @8.8.8.8 boe.ca.gov
; (1 server found)
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 59290
;; flags: qr rd ra; QUERY: 1, ANSWER: 1, AUTHORITY: 0, ADDITIONAL: 0

;; QUESTION SECTION:
;boe.ca.gov. IN A

;; ANSWER SECTION:
boe.ca.gov. 3774 IN A 134.186.249.87

;; Query time: 47 msec
;; SERVER: 8.8.8.8#53(8.8.8.8)
;; WHEN: Tue Dec 18 09:18:04 2012
;; MSG SIZE rcvd: 44

I can query ca.gov successfully from our servers.

Looking at this a little more the Authoritative servers for boe.ca.gov are

ns5.net.ca.gov
ns6.net.ca.gov
ns7.net.ca.gov

I can query ns6 with dig but not ns5 or ns7. All I get is “connection timed out; no servers could be reached”. I assume this could be my problem with resolving boe.ca.gov.

None of these servers respond to pings including ns6 and all traceroutes end in time outs(even ns6 that I can query).

Some suggestions please!