You do NOT, repeat, DO NOT need satellite or cable for HD. As of February 2009, all free tv will be required HD digital. Right now, most if not all of your local stations should come in HD. You may need to update your antenna (about 100 bucks for a long range one from RadioShack). The new antennas still recieve VHF/UHF signals until 2009 as well as the Digital signals.
Now, as far as the DVD player with tuner, it probably doesn't recieve HD signals, only VHF/UHF. This is fine until February 2009, when it will simply not work for tuning anymore. You'll still be able to watch/record DVD's, so no real issue there.
RadioShack employee; I also have an HD tv and an antenna for free tv......... I also will not pay 50 bucks a month when regular tv is entertaining enough. I did have to switch out my antenna to recieve digital though