Doesit display an IMEI number under the phone settings > general > status (something like this)? If there is no IMEI number then you have pretty much a phone that is no good for sim card usage and probably better off getting another phone if it's yours.
The logic board has the sim card reader on it, maybe it's an alignment issue with the board being installed not lining up with the housing properly? Usually this never happens, you have all of the board screw and antennae covers on the logic board clipped on right?
The bottom part of the phone also has housing that should be clipped and tucked in properly to gaurantee the antennas are contacting properly with the covers. Also the LCD cable from the screen needs to tuck in properly with the metal cover on top of it. Also make sure the metal midframe is not unclipped pushing either side the board / battery or LCD. There are like 3 clips for the metal to the housing frame on each side (excludes top and bottom).
Honestly IMO sony xperias are just as hard as doing HTC One M8/M9 screen replacements. Too many things can go wrong easily and you need to make sure everything is aligned, put in place, clipped in properly which is why I stopped doing screen replacements on HTC and Sony xperia in general. I still do Samsung from time to time but rarely even though it's easier to repair IMO.
- Breaking antenna cable or on logic board side (though you can avoid this easily of course by just pulling up the antenna cable from pulling cable instead of unclipping it with a nail from the end which will most likely break the antenna connector off the logic board.
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