...... I've fixed the problem. Here's a 'short' summary:
1) Problems with the BIND - I've fixed them using the info in this thread. Thank you!
2)No BIND in the service list. Bijo helped - thank you Bijo
3)Memory test, server restart , again problems with the BIND
4)Tried to fix with the info in this thread - didn't work
5)No named no bind in the service list. Bijo's advise helped again
6)Tried several times to fix the problem by changing IP addresses, updating DNSes & etc, but nothing helped. Whenever I edit a DNS zone (even if I don't make any changes)
the bind fails to reload. I tried both ways - editing the named.conf , running again all scripts & Cpanel update - no help at all. The IP addresses for both DNSes were correct,
and had the correct entries in /etc/nameserverips file.
7) Feeling helpless and hungry (no time 4 food), I did this (after checking again if everything is as it should be):
mv /etc/named.conf /etc/named.old
/scripts/rebuildnamedconf > /etc/named.conf
service named stop
killall -9 named
/scripts/fixndc
/scripts/fixndc
This (and I don't know why and how) fixed the problem.
The thing that is killing me is why it did not work the previous 4-5 times since my last post...
Being stubborn finally pays-off.....
Thank you for the help!!!! :p
I believe that the problem is in the fact that the server shared IP is xxx.yyy.zzz.254
and I could not use 255 for obvious reason

Therefor the 2nd ip address (the IP for the 2nd DNS) is .253...