If your cable box has an HDMI out that is all you need for the cable (not over the air HD though). Assuming your LCD does not have HDMI, just get an HDMI to DVI adapter and output the audio from the cable box to some speakers or receiver. Some monitors even have a source switch, so you can change between the analog and digital connections. Few notes to consider: Set the output of the cable box to reflect the widescreen. The aspect ratio might be 16:10 instead of the 16:9 of TVs putting little black bars on the top and bottom of the picture. Does your LCD support HDCP for protected content? Do you use the digital connection for your computer (you should be if you are running a high resolution)? Specs would help to define your setup…

Thanks for your input. I will try to find out the info you mentioned. You didn’t say I need a second or newer cable box from Comcast – don’t I need that?

Do you know which model you have now? When I used Comcast they gave me a Motorola box, that was years ago though. You can google the model by looking the brand up and comparing the pictures to yours. Since you only rent the box, if it does not have the output you need (HDMI) see if you can exchange it for a newer one that does. I would think that the current boxes they are handing out use HDMI out.
btw: I had an old Motorola DVR box (6214 I think it was) that even had DVI out, but I assume this question would not have come up if yours had one.