When you look at the video on the computer, does the remote resemble the one that you have at home? If not, you may have to reconfigure for a different remote to make those features to work properly.
You mention that you have an HDMI cable from the Slingbox to your TV. But how is the Slingbox connected to the cable box? Is there another HDMI from Cable box to the TV or is the Component cables connected?
If you have the Component cables running from the Cable box to the Slingbox, there is no way to get the channels to display on your TV until you have another set of Components from the Slingbox to the TV. This would complete the pathway for the audio/video to pass-through the Slingbox to the TV. This would require the video source on the TV to be set to Component as well.
Another way to have the audio/video to pass-through the Slingbox is to connect another HDMI cable from the cable box to the Slingbox and keep the HDMI from the Slingbox to the TV?
If you are wondering why there is one set of cables provided is because Sling Media only supplies one set. The Slingbox user has to supply the other set of cables.
Hope this helps!!!
Sling Media Moderation Team