I am changing my ISP currently DSL to Cable, and also will have a dynamic IP address as opposed to a static IP address previously offered by my ISP. I use a Slingbox Pro connected to my primary router and also a Slingcatcher in another country, again linked to my primary router on that network. What changes will need to be made to each device to keep it going?
You can check this article About static versus dynamic IP addresses
Basically it will be better to confirm with your ISP if you can change to a static IP, in that case you will not have any inconvenience to connect to the Slingbox remotely.