It sounds like you didn't actually do anything to make your gateway do any traffic routing... without instructions to actually route the traffic, it's not going to go anywhere.
You can do this with iptables.
You will need to have packet forwarding enabled in your kernel.
This will do the trick:
You'll also need to do some NAT. This should get you up and running.
echo 1 > /proc/sys/net/ipv4/ip_forward
If this works, you will want to apply the routing configuration at boot, which I like to do in a cron script @reboot. If you want help writing some iptables rules or making a cron script to run at boot, I'd be happy to assist you further with that.
iptables --table nat --append POSTROUTING --out-interface eth0 -j MASQUERADE
iptables --append FORWARD --in-interface eth1 -j ACCEPT