I have the same problem and I called Zenith for support. I was told that the ZBR716 does NOT have a "tuner", so the only way you can record what is on TV is if, and only if, the TV has OUTPUTS (3 connectors), which could be connected to the ZBR716's inputs. But then you could only record what is currently being watched on TV. You could not record and watch something else, or set up to record something at a particular time on a particular channel, because the TV has to be on.
Unfortunately, I didn't look into this until some time after I bought the unit, so I can't return it. I was told to get a VCR/DVD recorder WITH a tuner.
I, too, had a VCR with a separate coax connection for the incoming cable tv,and it worked like your other one did.
My fault for not looking into it sooner, Circuit City's fault for selling me something when I was very specific about what I wanted and what I wanted to do with it.
you can call zenith yourself, go to www.zenith.com
and hit the support page and eventually you'll find the phone number.