|"I strongly suspect the poor quality of the video is because of my TV tuner being Analog"|
Bingo! Analog cable TV will always look like crap on a high-resolution display, no matter how strong the signal is. DVD is considered to be the "bare minimum" for use on such displays. If you really want a good picture, you're gonna need a high definition source, like an HDTV tuner or Blu-Ray drive.
However, I wouldn't recommend getting a PC HDTV tuner. Because cable/satellite providers don't trust us, PC tuners are currently limited to receiving over-the-air (OTA) HDTV and unencrypted digital cable. When I had an HDTV tuner a couple of years ago, I could only pick up two 1080i OTA HD stations, and a few unencrypted 480i digital cable stations. Of course, all 60 of my analog cable stations were available, but they looked like crap on the HD projector connected to the PC.
I finally gave up on using the PC as a TV. Dumped the HD tuner and grudgingly subscribed to satellite HDTV service.