DVD/VCR and no cable box

I have Cable and only purchase the Expanded Basic.  I do not wish to pay $5/mo. for their cable box so plug the cable directly into my GoVideo dual DVD/VHs machine.  I use this machine to change the channels and just leave my Sony Bravia on channel 3.  My cable is not digital but is the same type everyone had 10 years ago - coaxl I think.  I did not want the cable company to upgrade the cable and pay for that too when they came through the neighborhood.  For the past few years now, whenever I watch a tv show,QVC, or a commercial and tell my VCR to copy a part of it, the show looks clear on my TV but when I re-play the VHS tape, it fades in and out; being good and clear for a few seconds and then falling into snow sort of like tracking used to do.  How can I fix this or what is happening?  I had heard that the cable companies were copy protecting HBO and such but regular cable too?  OR...is it my machine.  I tried to add a simple DVD/vcr player and then the TV went out saying - no signal.  Obviously I need very clearly explained help.