You should check proximity sensor, when you place call it should detect that you've placed phone close to ear and shut off screen to prevent you accidentaly pressing something on screen while you talking. By way you describing it, it looks like proximity sensor is triggered all the time, it can be because of bad quality replacement LCD, something that left between proximity sensor and glass. You should check that, also there is some software solution that can help:

https://talk.sonymobile.com/t5/Xperia-Z-...