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Settings > all > apps > smartconnect > clear data > restart the phone.
also, have you try different headphones?
repair the phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
If PCC doesn't solve your problem then you might want to contact your local Xperia care
http://support.sonymobile.com/global-en/contactUs/
also another thing to try is to boot on safe mode
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
@dilshankm
If you look carefully inside the 3.5mm jack , is there anything green surrounding the top?