Try doing a full charge (approx. 5h) then do a full 2-min restart (see [http://support.sonymobile.com/global-en/xperiaz5/faq/I-cannot-power-on-my-device/|here])
''Open the SIM card slot cover.
Using the tip of a pen or similar object, press and hold down the OFF button for 120 seconds, ignoring any vibrations, and then release the OFF button.
Charge the device until a charging icon appears on the screen.
Turn on your Xperia™ device''