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I suggest that you perform a software repair via PC Companion:
http://www.sonymobile.com/global-en/tools/pc-companion/
In PC Companion you press start on Support Zone > Start on Update the phone/tablet software > Repair phone/tablet (the blue clickable link in the message) > Follow these steps without having your device connected to the PC.
Follow the instruction that appears in the program and do not connect your device until this guide tells you how to connect it.
If the problem persist, you should visit nearest service center to have your Tablet Z examined by a technician. You can contact your local support team for further information about how to proceed with this in the best possible way:
http://www.sonymobile.com/global-en/support/contact-us/contact-info/
