In this case, as the first step we recommend you to hook up the Slingbox directly into your router. If it shows solid lights, it means that it is a healthy unit and the issue is related to your network connections.
Since the router is in a different room, we recommend you to use either a wireless bridge or the SlingLinks. The following link will provide you with all the information about the Sling Links.
Once the Slingbox gets solid lights, you will be able to run the Setup Assistant for Internet Viewing. Even though we have no information about your Slingbox model, you can check the following link in order to get the step-by-step instructions in order to know how to set up your Slingbox for Internet Viewing.