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The screen gets turned off during a phone call when the proximity sensor is covered. This is done to avoid accidental touch screen actions when keeping the phone close to the ear during the phone call. The proximity sensor is located in the top part on the display side of the device (e.g. Nokia N8-00, C6-01, C7-00, E7-00, Nokia Lumia phones).
If the screen gets turned off immediately when dialing a number or receiving a call, check that you are not covering the proximity sensor e.g. with your finger. Check also that there's no protective foil tape on the screen which would cause the proximity sensor to react too easily and turn off the screen when still in the process of setting up the phone call. If using 3rd party screen protectors, the protector may not be of the right size and will cover the proximity sensor, causing blank screen issues during the calls.