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Hi Jack, the coax going to a TiVo box would normally be a Virgin media cable and not a standard coax cable.
To address this you need to find a wall point which has a tv antenna linked to it and plug the coax cable between that point and the free view box.
With regard to the cable not being long enough this is an HDMI cable, they come in many different sizes, it sounds like the old one has developed a fault, I suggest you go to you local tv store and pick up a replacement 2m hdmi cable.
Please let me know if you need anything clarified.