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Both of my Sony RDR HXD 890 recorders now only show a blank screen from 12.12.17. What can I do to get a picture back
That sounds very strange. My first thought was whether some unexpected change to the Freeview platform had occured as this has been the cause of issues in the past, however my HXD870 seems OK (just checked).
If both your machines are on separate systems then I have no logical explanation. If they are in the same room then make sure you haven't selected an external line input or done something using a common remote control.
If you have no menus showing then you need to trouble shoot just one recorder. Nothing makes sense when two machines fail simultaneously.
You have to begin from scratch and confirm correct connection to TV and select appropriate input on the TV. A factory reset is one option but it seems illogical when the two machines are both doing the same.