At the very least we would need the make/model/cable provide to know what possibilities may exist ;).

My gut feeling says that any cable co box firmware/DVI out port will not support the correct DVI output to make a conversion possible as you desire. Also, what cable provider lets you buy/bring in your own box(??) That is limited to Satellite providers, at least in the U.S. AFAIK. Keep in mind simply because a device is depicted with a particular port, that doesn't mean it is active. The USB ports present on the various Motorola DVRs is a good example of this.

Another place to ask would be a user support forum for your cable provider, as well as AVS Forum. IME is also a strong site for general issues like this one.