Snow? On a modern video device? Zero signal should produce a blue screen, not snow. Snow is generally RF static from a tuner that isn't connected to an antenna, or is tuned to a blank channel.

Let's do a bit more investigation.
1. Play back a commercial DVD. OK? DVD side works great (so the connections are OK) 2. Play back a tape recorded on some other VCR, or a commercial tape from Blockbuster. OK? If not, it's the playback heads or something in the tape transport mechanism. Just get snow and audio
3. If step 2 worked OK, try recording a tape from DVD. What's the result? Still snow If it's snow, it could be that you simply have something wrong in the setup, and are recording from an unconnected RF input, rather than the DVD. DVD and VCR are the same unit, no outside connection between them. If it works OK, then
4. Try recording a tape from a signal on an external input. Still snow and audio If you get snow, then once again check your setup.