Here is an HDMI capture card. Its only $250. But its in a very questionable area legally if its used to capture "protected" content. And the uncompressed HDMI stream will eat hard disks really fast if you can even record it. It doesn't encode to
The card probably isn't capable of capturing "protected" content (i.e. doesn't do HDCP), that would defeat the purpose of the content protection. So you're probably still "up the creek" with respect to the cable box as I imagine it will output any HD signal protected with HDCP (there are ways and means but these are certainly legally questionable.).