It seems that you are having some issues in order to get the connection to your Slingbox ever since your new service provider installed a new modem.
Whenever you install a new modem or router, you need to reset your Slingbox in order to clear out all the "old" information (the old IP address provided by the router). Then, you need to run the Setup Assistant for Internet Viewing in order to use the new IP address provided by the router for your Slingbox. The following links will provide you with the steps to follow:
Hope this helps!