If you have RGB cables going in to the Slingbox (make sure they are on the input and not the output) then you need to add similar cables going out from the Slingbox to your TV. You need to be able to see the television stream on your own television first. If this doesn't work and you can't see your own signal as it is looped straight through the Slingbox, then the cables are not connected properly. That is the only possible answer if your tv does not show a picture.
I did not even know that the Slingbox has an optical audio connection, but I would do away with that until you fix the picture problem first. Remove the audio connection first and see if you have a picture first, then worry about the audio.
But it is very important that you wire the system correctly. You say "The TV is connected to the Direct box via HDMI." so I want you to disconnect this cable for now. Now you must wire the system so that you are able to watch television through the Slingbox connections and not through a direct HDMI connection where you are bypassing the Slingbox.
Once you get the connections correct and you can see and hear video using a different auxillary input RGB (not your HDMI) then you will probably have no problems watching it on the internet, provided you can watch other inputs on the internet properly. After this point where the wiring is correct, and you can see and hear the television using a RGB input on your TV (not the HDMI), then you can safely remove the RGB wires between the Slingbox and your TV and plug the HDMI connection back in. Then leave it that way and then you will be watching with HDMI at home, and with RGB while on the internet or mobile device while on the road.