Basic problem is that the Zytel P600 will allow internet connectivity although not when connected with another router.
The problem is most likely due to a conflict of IP addresses. For example, many Zytel modems will use 192.168.1.1 as their default IP which conflicts with many Linksys routers.
To solve this problem you'll need to do 3 things:
1) Change the IP address on the router to something outside of the Zytel modem range. 192.168.1.254 worked for me although you could try 192.168.0.1 or 192.168.2.1.
2) Disable DHCP on the router. The Zytel wants to be in control of the DHCP.
3) Connect the Zytel to a regular port on the router instead of the internet port. This allows the Zytel to be in control of the DHCP and the router basically acts as a passthrough hub.