LinuxQuestions.org - DNS problem. Please help!

Hi,
I have followed several tutorials but still can't get it to work. Could somebody help me with this?
Basically 10.0.0.x is on DMZ, and 192.168.0.x is our Intranet. I am building a Red Hat Linux DNS server sitting on DMZ side. My goal is to putting this Linux box as our internal DNS server to get reduce outbound network traffic.
When I start named service, no errors recorded in /var/log/messages/, it says started successfully. I can resolve names as well as www, client....on the Linux( ns ). nslookup & dig commands indicated NOERROR on "status" field. But if I set up my workstation( client ) to use ns as the only DNS server, and I run nslookup on client, error message: nslookup ***Can't find server name for address 192.168.0.100: No response from server. *** Default servers are not available. Default server: Unknown Address: 192.168.0.100 google.com Server: unknown Address: 192.168.0.100 *** Unknown can't find google.com: No response from server. Do you see any mis-configuration on my files?
Also, when I do "host -l -v -a mydomain.com", I got "Connection to 10.0.0.1#53 failed. Connection refused." However, I use "nmap -sS localhost" I can see port 53 TCP is open so firewall is not blocking it, I guess? Why do I get this error message?
Thanks.
Frank

Here are my config files or related files:
1. /etc/hosts:

127.0.0.1 localhost
10.0.0.100 ns.mydomain.com ns
10.0.0.150 client.mydomain.com client
10.0.0.9 www.mydomain.com www
10.0.0.10 pec80.mydomain.com pec80

2. /etc/resolv.conf:

domain mydomain.com
search mydomain.com
nameserver 10.0.0.100
nameserver 127.0.0.1
nameserver ISP's name servers

3. /etc/named.conf

options {
directory "/var/named";
pid-file "/var/named/named.pid";
listen-on {127.0.0.1};
allow-query{any;};
forwarders { ISP's name servers; };
};

//
// a caching only nameserver config
//

zone "." {
type hint;
file "named.ca";
};

zone "mydomain.com" {
file "named.hosts";
type master;
allow-query {any;};
allow-update{any;};
};

zone "priv.mydomain.com" {
file "priv.named.hosts";
type master;
allow-query {any;};
allow-update{any;};
};

zone "0.0.127.in-addr.arpa" {
type master;
file "named.local";
allow-query {any;};
allow-update{any;};
};

zone "0.0.10.in-addr.arpa" {
notify no;
type master;
file "named.0.0.10";
allow-query {any;};
allow-update{any;};
};
zone "0.168.192.in-addr.arpa" {
notify no;
type master;
file "named.0.168.192";
allow-query {any;};
allow-update{any;};
};

};

Under /var/named/, there are:

1. named.hosts:

@ IN SOA ns.mydomain.com. hostmaster.mydomain.com.
{.............................
}
NS ns.mydomain.com.
MX 10 pec80.mydomain.com.
localhost A 127.0.0.1
ns.mydomain.com A 10.0.0.100
pec80.mydomain.com A 10.0.0.10
www.mydomain.com A 10.0.0.9
client.mydomain.com A 10.0.0.150

2. priv.named.hosts:

@ IN SOA ns.mydomain.com. hostmaster.mydomain.com.
{.............................
}
NS ns.mydomain.com.
MX 10 smtp
smtp A 192.168.0.10
pec1 A 192.168.0.4
pecsbt A 192.168.0.8
ftp A 192.168.0.88

3. named.local:

@ IN SOA localhost. root.localhost.
{.............................
}
IN NS localhost.
1 IN PTR localhost.

4. named.0.0.10:

@ IN SOA ns.mydomain.com. hostmaster.mydomain.com.
{.............................
}
NS ns.mydomain.com.
100 PTR ns.mydomain.com.
10 PTR pec80.mydomain.com.
9 PTR www.mydomain.com.
150 PTR client.mydomain.com.

5. named.0.168.192:

@ IN SOA ns.mydomain.com. hostmaster.mydomain.com.
{.............................
}
NS ns.mydomain.com.
3 PTR smtp
4 PTR pec1
11 PTR pecap1
8 PTR pecsbt
88 PTR ftp