Welcome to the answer forums. With you changing the router the Slingbox is hooked to it is saving the old IP address. I have a few steps that I would like you to look into and this should get your Slingbox up and running for you.
After the hard reset please go to setup.slingbox.com and walk through the setup
After you do this the Slingbox should be able to connect and be able to watch with no problems.
Sling Moderation Team
I am having the same issue as well and would like a straight answer from sling box. They act like their device will work with any router but I don't believe that at this point. I have the sligbox hd pro and my router is the Netgear nighthawk R7000 I have done every step for resetting the sling box and wasted hours trying to get it to function. When the sligbox is plugged into the the router its port led glows amber ON the router. This is an indication that the device is not fast enough for the router, meaning the router is too good for the slingbox HD pro. IF I AM CORRECT, which after many hours of looking online to try and get a straight answer, then this will NOT work with this router. If someone at sling box would PLEASE just say this rather than making me and many others waste a day of our lives troubleshooting an impossible thing PLEASE DO TELL and that would be a little less insult here.