Inside Sling Box TV Streaming

How can I make cable box transmit signal over HDMI AND Component output at the same time (keywords:same time)?

I have 3 items to connect: Magnavox 37MF231D/37B, my Scientific Atlanta Explorer 4250HD cable box and my Slinbox Pro HD (300-100)
I have stumbled upon a problem: when cable box connects to TV via HDMI cable, it blocks out all other video outputs such as component video, so I cannot use it to connect it to my Slingbox. I can not use component (blue,green and blue) and composit (red and white) audio cable to connect to my tv, since this combination creates sort of a loud static noise from my tv speakers (no problem though when I connect it via HDMI or Coax). So I need to figure out a way to connect my cable box to tv via hdm and at the same time connect to my slingbox via component cable.

Does this mean I am going to have to purchase 2 additional things:
http://cgi.ebay.com/3-RCA-RGB-Component-... - this is a component signal splitter.
and then something like this: http://www.newegg.com/Product/ShowImage.... - to convert component into hdmi (for tv)?

this seems like it will work, I am just worry about signal loss when i connect all those together. Any ideas as to what I can do or how can I simplify this. Hack the cable box may be???
Thanks, but my TV has problem with component video input once I plug it in speakers make static noise along with the sound, I know component cable doesn’t carry the sound but that’s what it does only when I use it. So I decided to go a little bit long way, just bought a component signal splitter, then I bought component/spdif to hdmi converter adapter. This way I will have component going to slingbox and hdmi to TV: perfect. I am just worried about loss of signal if I am using 2 adapters in between cable box and TV