Everyone buys their TiVo unless you've got one thru your cable company.
It might be better put that you avoid the monthly fee by buying a Lifetime Subscription at the time you get the box...or shortly after that.
Your 2160 does have a digital QAM tuner-I've got one, recording NCIS LA right now. Click the DTV/TV button on the remote to switch from the analog channel tuner, to digital. Only your local broadcast TV station's HD channels, their digital sub channels, plus WGN, and perhaps a few shopping channels will be available...the basic cable chs will not. You will now have to record those basic chs like TNT, USA, ESPN, with the cable box feeding one of the recorders line inputs. The cable from wall to a splitter, then one to the 2160's RF jack, the other to the cable box, then composite cables-yellow video, red/white audio, from the cable box to the back of the Magnavox. Note-the small DTA cable boxes will not have composite outputs, which means you can't split the raw cable to both the Mag and the DTA, which renders the recorder's tuner useless as it won't have it's own signal in order to view/record the local HD stations.
You may need to run a ch rescan since it seems, you've never used your May to record those QAM chs.
The QAM channels that will be left after Concrap transitions your system, in the digital tuner will not have the same ch number as the analog channels do now. A full rescan Under the Setup menu will be needed. Once completed, only the active digital channels will be shown-after the scan is done, it will land on the first available QAM channel. Use the ch up button to surf what your line up ends up having.
Note to Newbies:
Who knows for sure, but the correct answers to these questions are: