I tried to turn on my iPhone XS; I succeeded but now that I have closed it again the display works but not the touch.
It doesn't matter where I touch, it doesn't work. The rest of the phone works, however.
What could it be?
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There are only two pathways to address this:
Reset your phone. Obviously, you need to make sure you have a backup of your data.
You need to take it in for service. The Apple employee will actually repeat step one (and inform you about making a backup as well).
The digitizer (the portion that detects touch input) has died. Unfortunately, it's no longer a separate components, but it's now glued to the LCD (the portion that displays images). The whole assembly will need to be replaced.
There is a possibility that the logic board malfunctioned and the digitizer and display is still good, but without opening it up and putting hands on, it's impossible to tell - you still have to take it in.