I agree with Kevin on the copy-right protection. HDMI was fundamentally created to prevent recording. If your device is just a TV or monitor...fine...HDMI will toss keys back-and-forth to enable viewing. I'll assume your convertor...the HDMI endpoint...just isn't responding to protection negotiations.
A computer by nature is a recording device because it has storage; therefore, there may be no copy-right protection on its hardware but instead its software. For example, if you wanted to watch Cox programming via a computer, you're probably limited to watching via Cox software...which has no recording ability.
I don't know much about HDCP but I'd assume your cable box just doesn't like the convertor.