the internic records for our domain is like

domain: mydomain.com
ns1: ns.liquidweb.com
ns2: ns1.liquidweb.com

ns.liquidweb.com have records for our server so i can reach my server.

and we have dns server registered to internic also
ns1.mydomain.com
ns2.mydomain.com

we have records on our server dns zone as
;$TTL 14400
@ 14400 IN SOA ns1.mydomain.com
20050441506
14400
7200
3600000
86400


Domain TTL Rec

mydomain.com. 14400 IN NS ns1.mydomain.com.
mydomain.com. 14400 IN NS ns2.mydomain.com.
mydomain.com. 14400 IN A 192.168.1.2
localhost.mydomain.com. 14400 IN A 127.0.0.1
mydomain.com. 14400 IN MX
mail 14400 IN CNAME mydomain.com.
www 14400 IN CNAME mydomain.com.
ftp 14400 IN CNAME mydomain.com.
host 14400 IN A 192.168.1.2
ns1.mydomain.com. 14400 IN A 192.168.1.2
ns2.mydomain.com. 14400 IN A 192.168.1.3
ns1 14400 IN A 192.168.1.2
ns2 14400 IN A 192.168.1.3


but i can't ping to my name servers. and dns lookup is failed too.
as support says, i have to change my domain names internic records as

domain: mydomain.com
ns1: ns1.mydomain.com
ns2: ns2.mydomain.com

And then i will be able to reach my dns servers and dns lookup will resolve the name servers.

Is this the way that i must go? Or is there a way that my domain names internic records remain the same but i can also use my name servers?

you can point your nameservers to the same IPs of liquidweb nameservers and see how it goes.

nice tools to check remotely are www.dnsstuff.com www.dnsreport.com www.checkdns.net www.dnscheck.com etc..

Bashar is right