Hello, do they make an adapter to go from hdmi to coaxial cale? cable box to tv
More aboutdigital cable coaxial
Call the cable company and ask for a newer cable box. You are renting it, and the upgrade should be free. But even new TVs should have a coax connection, you sure you don't have one?
It seems that you have a non HD TV and an HD cable box without RF output. It should have non HD outputs such as composite video. If not get an non HD box from your provider and that should have an RF output.