Could you show us the the contents of /etc/sysconfig/network-scripts/ifcfg-eth0 and /etc/sysconfig/network-scripts/ifcfg-eth1?
ifcfg-eth0
DEVICE=eth0 BOOTPROTO=none BROADCAST=xx.xx.xx.xx IPADDR=xx.xx.xx.xx NETMASK=xx.xx.xx.xx NETWORK=xx.xx.xx.xx GATEWAY=xx.xx.xx.xx ONBOOT=yes TYPE=Ethernet USERCTL=no PEERDNS=no
ifcfg-eth1
DEVICE=eth1 BROADCAST=xx.xx.xx.xx IPADDR=xx.xx.xx.xx NETMASK=xx.xx.xx.xx NETWORK=xx.xx.xx.xx BOOTPROTO=none ONBOOT=yes TYPE=Ethernet USRCTL=no PEERDNS=no
Both have static IP addresses. One is external to a DSL connection and the other Internal to a DMZ.