Disconnect the battery. Double check the connector on the flex of the LCD and the connector on the board - checking for any bent pins. If they all appear fine then test a new LCD to see if your getting the same result.

I would redue the part on the assembly guide that shows you how assemble the front facing camera and ear speaker - ensure that everything is snug and aligned properly as seen in the guide. When you go to boot the device instead of just turning your device on preform a soft reset to boot the device.

Unfortunately your device will need a new screen assembly (lcd/digitizer). With the phone being so new it will be hard to track down the part. Check with Sony directly.