If you used the Oppo's cable with the cable box and it worked, how about the other way around? have you tried a DVI-DVI cable with a DVI-HDMI connector on the Oppo's side?
It will only cost you the price of a DVI-HDMI adapter to test.
That's how my 970HD is connected.

Just curious. Did you install the latest firmware on the Oppo? I am wondering if this is some sort of HDCP-related problem.