I understand that you are having some issues with your network configuration since it has routers. Even though the Slingbox shows solid lights, you are not able to get the connection.
The fact that the Slingbox shows solid lights indicates that the Slingbox is a healthy unit. With this in mind, I recommend you to check the following links in order to get the related information and steps to follow.
If the issue persists, I recommend you to reset the Slingbox and run the Setup Assistant for Internet Viewing.