You can't record HD to tape or disk (DVD media) so what you have is fine for recording.
My DVR does not require a satellite but there are cables to/from the cable company and my TV.
We have HDTV, but no satelite or cable service. I just want to tape a few shows from network TV. Will Tivo or DVR's work without cable/satelite? Our VCR/DVD player is older and doesn't really work with the HDTV, so we need to do something different, but we get a different answer from every TV sales guy we ask.