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Are you able to start the camera by pressing the camera application? If yes, I suggest that you go to Camera > Menu button (three verical dots) > Go to the tools tab > Make sure that the option "Quick launch" is not Off.
If this wont help, do you experience the same behaviour if you boot your phone into safe mode?
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
