I understand that you want to know if you need to adjust any other settings if you have a new cable service provider.
If you have a new router, you'll need to run the whole setup one more time. If you have only changed the set top box, you will need to run the TV Input configuration.
Keep in mind that every time you get a new router, the Slingbox will get a new IP address. This means that you will need to run the Setup Assistant for Internet Viewing in order to adjust the new router settings. During this process, you will select the specific make and model for your TV source (cable box, DVR or satellite receiver). If this is your case, you must go to setup.slingbox.com in order to run the Setup Assistant for Internet Viewing.
On the other hand, if you have just changed the cable service provider, you need to run the TV source configuration. This process will allow you to select the settings in order to control the new set top box with your Slingbox.
In all case, once you finish any of these processes, you must go to www.slingbox.com and click on "Watch" in order to get the signal from your Slingbox.