Hi @Milo2, sorry to hear about this. 
Do I understand correctly that as soon as you tap on the call button, the screen turns off and does not turn on again until the call has ended?
There is a small sensor on the device that will turn the screen off during a call, for example, when it's covered by your ear. If there is any dirt or moisture or the sensor is covered by a case or screen protector they screen will turn off directly when you make the call, instead of when the sensor is covered.
On the link below you can see where this sensor is on the device and make sure that there is no dirt or moisture on the sensor and that nothing is covering it. It's number 4.
https://support.sonymobile.com/global-en/xperiaz3/userguide/phone-overview---d6603d6653/
Let me know if that helps!
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