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Hi,
Please take a look at the following topic for some advice regarding USB connection problems:
http://talk.sonymobile.com/t5/FAQ/USB-connection-problems/m-p/348074#U348074
In that case I suggest that you try with a different USB cable and if that doesn't work, I suggest that you try to connect the phone to another computer.
Well in that case you might need to have your phone examined by a service center. Please contact your local Xperia support team for more information on how to find your nearest service center:
http://www.sonymobile.com/global-en/support/contact-us/