Internal container cannot reach Internet
Supposing you have connectivity to other addresses of the host, probably you need to set up some kind of NAT.
There is plenty of ways to do it, (check links in the references). One that requires little asumptions about the case is to
MASQUERADE the packets with
In this case the "NATed" network is
iptables -t nat -A POSTROUTING -s 10.0.4.0/24 '!' -d 10.0.4.0/24 -j MASQUERADE
Linux 2.4 NAT HOWTO: Saying How To Mangle The Packets