As I understand it, athough the HDMI provides a Menu output, as far as Live TV is concerned it is aimply a pass-through. As such you need a TV signal on the HDMI IN to use the HDMI OUT. As you are actually feeding the Component IN with your TV signal you will need to use the Component OUT to drive the TV.
Thank you for using our answers forum! I'm sorry to hear you are not getting a video signal when attempting to watch live TV with your Slingbox 500. The reason you are experiencing this issue is because the way you have you Slingbox connected. Hooking up Component from your cable box to your Slingbox then HDMI to your TV will cause this issue. It will allow you to setup, but it will not stream Live TV. You will need to connect the same type of cables on the OUT and the IN on the Slingbox in order to stream on your TV. For example, if you would like to use HDMI, you would want to connect HDMI OUT of your cable box to the IN on your Slingbox. Then, you connect another HDMI from the OUT on your Slingbox to the IN on your TV. This will give you audio and video when connecting to the Slingbox as well as on your TV. You always need to have the same type of cables when attempting to pass video through to your TV. Below is a link to the 500 quick start guide. This tells you how everything should be connected.
Hope this helps!
The Sling Moderation Team