Using an HDMI video source with the Slingbox 500 (even though you have a Slingbox 350, the basic tenets of the article apply)
and RNG200N Outputs for someone else asking the same question. In short, use component cables for video to the Slingbox and then pass that video through to your TV. Hopefully your TV has component video input and your cable box can feed audio (if you're using the TV's speakers) to the TV via a cable the TV can accept.
Possibly someone with a RNG200N can respond as well.