SIM and signal problem

Well I can say at least the antennae is not causing the issue as you have already replaced that.

Does it 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.

I'll just relist these even if they have been mentioned already:

Not detected sim card:

- Bad sim card (Could be just faulty, dirty, physically won't fit or line up with the pins properly)

- Sim card reader could be damaged, either on the housing of the reader that wont let the sim sit on the connection pins properly, misaligned or missing pins.

- Incorrect sim card tray being used if this sony xperia model uses it. (Could also be upside down, wrong way orientation of tray or sim card etc).

- Very highly unlikely but maybe network locked phone. Was it working before you did the screen replacement?

While I have done a few of Sony Xperia Z3 screen replacements in the past LCD only and LCD with frame I find it hard to manage to get the sim card to not read properly after that.

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.

My sony repair history

- Broken mic flex, did not install antenna cover properly causing no signal issue on 3G / 4G.

- LCD getting damaged on improperly installation / lifting up LCD

- 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.