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Check your SIM card is correctly seated and free from dirt etc - Also is your card a correctly manufactured one or have you cut it down to size? as a loose fitting or ill fitting SIM card will do this
I tried taking the SIM out and replace it, did not work I made sure that my SIM was clean and did not work, I tried it without SIM in the phone and it keeps turning off
Sorry to say but in circumstances like this you need to either return your device to the place of purchase or contact Xperia care http://www.sonymobile.com/global-en/support/contact-us/
I found out what the problem was the conection with the battery is broken and I am having it repeared but thank you for the help