Hi,
Turn on the phone and then try shining a torch at an angle close to the screen and check if you can see images at all on the screen.
They will be very faint if they are there so trying this in a darkened room may help to see them.
If you can then you have a backlight problem.
It could be in the new display (faulty unit), a blown backlight fuse on the systemboard (was the battery disconnected before reconnecting the new display?) or another problem on the systemboard.
I couldn’t find the schematics for your model but here’s a link showing the backlight fuse location for a Xperia XZ2 that may help. Hopefully it may be the same for your model. [post|611032].
As a DIY repair all you can do if it is a backlight power problem is to check if there is backlight power going to the display i.e. fuse OK and if so replace the display.
If there is no backlight power at all then you would need the schematics for your model to find out what’s wrong.
''If it is not a backlight power problem and there is no display at all'' then you could try another display and check if that works (faulty first replacement?) and if still not working then it is a systemboard problem.