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The 3 vibrations indicates a forced switch off - Check the volume up key and power buttons aren't been pressed down
Bit of a long shot but remove your sim card and sd card if you have them inserted and then try starting the phone
Also on the side under one of the flaps in a red reset button - Try pressing this and see if that works - Failing that you could try a system repair and if that fails then all I suggest is to return it to the place of purchase or contact Xperia care http://www.sonymobile.com/global-en/support/contact-us/
i am having a prblem with my phone too, it doesnt turn on
i have tried the power on with volume up and with volume down
even the red reset botton by the sim, it still doesnt work