With your original connection, you are asking Slingbox to convert an analog signal to digital in order to display on your TV. I don't think it can do this. Please someone correct me if I'm wrong. HDMI should be passed thru unaltered in your second connection scenario, so its not surprising that HDMI in-->HDMI out worked.
I am getting a similar problem. I had it all set up and everything was working for weeks and then it stopped working when I just try to watch tv. I can still get sligbox on my computer and do everything but cannot just watch tv. I have my cable box hooked up with both HDMI and Component and then HDMI hooked up to my tv (via a receiver). I had component hooked up from slingbox to tv (via receiver) as well and that also did not work. When I went back to setup I could see the small tv image that shows up but then when I switched to live tv I lost the signal and tv went blank.
Thank you for posting in our answers forum! I'm sorry to hear you were not getting a video signal on your television. Being that you need to use component cables from your set-top box to your Slingbox, instead of HDMI, to avoid HDCP; you will need to add another set of component cables to the OUT on your Slingbox, going to your television. Also, you will need to switch the input on your television to component. If you connect it this way, you will get a video signal on your TV. Being that there is no HDMI from your set-top box to the Slingbox, you will not get a video signal if you use HDMI from your Slingbox to the TV.
Hope this helps!
The Sling Moderation Team