I'm sorry for not perfect english. In time I'll do a good quality translate. If you could not get anything please feel free to contact me in comments. I will answer you as soon as possible.
First of all analyze and pick up the phone jack ( without going into details, because all phones are different) . Incidentally, a similar problem is described by the example number Sony Ericsson Xperia MT15i ( SIM-card slot ).
It looks like the connector in this case, six out of six " antennae " broken off .
Remove excess plastic parts, not to hinder . Could be done " in good"-unsolder all of the metal connector housing and remove with plastic. But you can get a neat broken off extra plastic parts. Every case is different, it is not always acceptable.
Unsolder the old contacts .