Arris sbg10 shows all green lights but is not connect to internet

Do you have device connected to the modem Wi-Fi network or to the modem directly? If yes 

You can access modem GUI to check the WAN IP address to check on your case further.

Launch a web browser, such as Internet Explorer, Firefox, or Safari.  Enter http://192.168.0.1 into the address box.  The Login page will appear.  
On the Login page, enter password in the Password field then click the Apply button.  

click on the WAN setup tab and you can see the WAN IP address.