It might be true, that support generally takes ages to answer, but in your case that seems not to be true. Faulty phone about one week ago and support already replied, that warranty is over.
In your case I really would not accept that reply from support without complaint.
Call them (numbers to be found in the thread contactsupport) and ask again.
The partially not responding touchscreen really is a more common issue; as the following thread with 275 postings proves:
That makes me rather suspicious. that this kind of thing is a design or production flaw. And I guess, that did not change the supplier and the design for no reason.
Therefore offering them the 40 Euro might be an acceptable solution for FP as well.