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So you press the power button? You might have enabled power button ends call.
Does this happen when you place the phone to your face/ear to answer the call & the contact with the screen opens various apps etc?
Boot on safe mode and check again
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
There is an option in accesibility called like that.
In this case,boot in safe mode and keep us updated.