I've just looked and this recorder does have it's own digital tuner, so you should be able to record one digital channel and watch a second using the TV's own digital tuner.
I'd first ensure the aerial feed links to both digital tuners. I'm not familiar with the HDMI connection, but the recorder should be able to operate without this connection. Will the TV display a digital channel with this cable disconnected and whilst the recorder is recording another digital channel?
If yes, the aerial connections seem to be OK