Tested for you before leaving work tonight. No loss of Team Rock Radio with the Rear on so I headbanged the whole way home :-D
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I'm going to try it tomorrow when I'm in the centre of Glasgow. Could be that my house is in a marginal signal area.
Pretty sure the aerial is in the rear window, think that's what the vertical lines are.
I had the same problem. Seat informed me the antenna for the DAB runs through the rear screen and can short. They replace the back screen
Just had mine done last week and now working fine with the DAB and rear screen heater on.
They are aware of fault
Hope this helps