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It may be a issue with the charging port - If it is still under warranty then return it to the place of purchase or contact Xperia care http://www.sonymobile.com/global-en/support/contact-us/
If you are able to connect the phone to your computer, I suggest that you try to repair the phone software using PC Companion..
Before repairing your device you may want to backup your information first. Check out this topic for more information on how to.
How to backup?
If the issue should still remain I think that this needs to be examined and fixed at a repair center. For more information about how to submit your phone for repair and where, contact your local support team.
same problem faced by me. Firstly Sony care center suggested to update your mobile or reinstall the software . Then from this software updation no outcome is there. Finally then they suggests to change the motherboard of your phone then also problem is not solved. Further i don't know actually i faced also this exact problem with Xperia L and i am facing this trouble too but all these above solutions are done by Care Center. But the problem is not solved. Now the only and final outcome is there that company has to replace my phone otherwise.