DVD connections and snow on screen

Yesterday we bought a Mitsubishi DVD player. When we got it home, I hooked it up to the TV, which is also a Mitsubishi. It came with three cords with yellow, red, and white plugs, and the manual showed how to connect what with what.
Unfortunately, although the DVDs play just fine (and even the sound is good), the broadcast stations have snow on the screen. We have a Zenith VCR in-line between the antenna coaxial cable and that connected to the TV; I know about the “Input” procedure requiring use of a switch, on the TV, to switch between the antenna (to which the VCR is in-line) and the back-of-TV set connections for the DVD player.
How do I get the DVD player to be hooked up and operate, without spoiling the picture we get when we want to view broadcast stations?