First, make sure you can ping the machine your Z is connected to.
If you can't, do an ifconfig on each machine to make sure both interfaces are up, and using the correct ip addresses.
Second, make sure you can ping your dns servers.
If you can't, you may need to set up iptables on the host machine. Make sure your kernel and distrobution have support for iptables enabled. Check
this thread for instructions on what to do after that.
If you can ping your dns servers, make sure your /etc/resolv.conf looks like this:
namserver 198.164.30.2