I meant how did you get these IPs, from a dhcp server or from a router/fw ? As you said it, running iptables has nothing to do with your problem.
What's the config now ? The new one should be on the same network, no ?
If you really have to change it now, you could issue the command :
root@machine# ifconfig eth0 18.104.22.168 netmask 255.255.255.0 broadcast 22.214.171.124 ; ifconfig eth0.1 126.96.36.199 netmask 255.255.255.0 broadcast 188.8.131.52
thus you'll configure the 2 IP on the same nic... keep the hand on it and then see which is in use
2 other ideas :
Don't you have the IP of the gateway ? It should be on the same subnet as one of the 2 IPs.
You can also learn the different subnets by doing a traceroute to the server....