It seems that you are having some issues in order to get your Slingbox up and running ever since you replaced your old router.
Whenever you connect a network device to your router, it will assign an IP address to the connected device. This way, the device will be able to reach the Internet service.
This means that if you have connected the Slingbox to the new router, you will need to reset the Slingbox in order to clear out all the "old" information provided by the "old" router. This way, you will be able to identify the new IP address provided by the router for the Slingbox and you will be able to run the Setup Assistant for Internet Viewing. The following links will provide you with the steps to follow in order to fix this issue and set up your Slingbox for Internet Viewing:
Make sure to check these links and follow the recommendations. Let us know how it works for you!