How to properly configure network interfaces (Internet and LAN)?

Question

network hardware

Good time of the day.
There is a server with CentOS 6.5 and two network interface cards.
eth0 - accessible from outside (108.0.0.100 )

EVICE=eth0
ONBOOT=yes
BOOTPROTO=none
NM_CONTROLLED=yes

PREFIX=25
IPV6INIT=no
DEFROUTE=yes
IPV4_FAILURE_FATAL=yes

NAME="System eth0 - Internet"
IPADDR=108.0.0.100
GATEWAY=108.0.0.10
NETMASK=255.255.255.128
DOMAIN="108.0.0.1 108.0.0.2"

eth1 - available on localhost (192.168.0.123)

EVICE=eth1
ONBOOT=yes
BOOTPROTO=none
NM_CONTROLLED=yes

PREFIX=24
IPV6INIT=no
DEFROUTE=yes
IPV4_FAILURE_FATAL=yes

NAME="System eth1 - Local"
IPADDR=192.168.0.123
GATEWAY=192.168.0.10
NETMASK=255.255.255.128
DOMAIN="192.168.0.1 192.168.0.2"

It is not possible to make the server normally look at the Internet (now it is visible from the outside, but it is not possible to access more than one resource from it).
PS nslookup google.ru command now gives this

;; connection timed out; trying next origin
;; connection timed out; trying next origin
;; connection timed out; trying next origin
;; connection timed out; trying next origin
;; connection timed out; trying next origin
;; connection timed out; no servers could be reached

Answer 1

Show the output of the commands:

ip a
ip r
iptables-save