It seems that you are having some issues in order to set up your Slingbox for Internet Viewing since you do not have access to the local router.
In this case, if you have no access to the router, you will need to get a wireless bridge. You will connect the wireless bridge on the back of the Slingbox and you will be able to get the wireless signal sent by the wireless router. You will also need to make some adjustments in the router settings in order to enable the Internet Viewing feature.
Finally, keep in mind that the router is the only network device that provides the IP addresses. This means that if you cannot connect to the router, you will not be able to set up your Slingbox for Internet Viewing.