It seems that you are having some issues with your Slingbox, since it does not get the solid network light when connected to a switch.
In this case, since you have already tested a different connection to your router and the Slingbox gets the solid network light, the issue seems to be the connection through the switch.
As an option, we recommend you to use the SlingLinks or a wireless bridge. If you decide to get the SlingLinks, you must verify that both rooms (where the router and the Slingbox are) go into the same electrical circuit, otherwise, the SlingLinks will not work for you. You will be able to get further details on the following links.