I understand that you are having some issues trying to configure your Slingbox PRO-HD for Internet Viewing with your new Netgear N600 router.
In this case, I recommend you to connect the Slingbox to the new router and reset the Slingbox.
Once you follow this recommendation, you will be able to locate the IP address provided by the router for your Slingbox. Now you will be able to create the rule that will allow the communication between your Slingbox and the Internet service. Since you did not provide any information about the specific model number for your router, I encourage you to check the following third-party links in order to get further details that might help you: