It sounds like you've done a fair amount of troubleshooting already. However, not all HDMI to Component converters are guaranteed to work with Slingbox. Here is some information on the one we know does work:
If this is the one you're already using, there may be something going on with one of the cables; either the HDMI cable between the DirecTV and the converter, or the video cables between the converter and the Slingbox.
Also, if you haven't already, try giving a reboot to the cable box.
Lastly, make sure the Slingbox is properly configured to accept a component signal. You can run through the process found in this article just to be sure (don't worry about its title):
Hope this helps!
In that case, check out this article:
If that doesn't work, try this article: