In cases where there are "no signs of life" I always try a few things.
# Connect to a computer. Is it detected in any way? Check File Explorer, Device manager or Disk manager on a Windows machine if it doesn't show in iTunes. Use Finder, Disk Utility, or System Info on a Mac. This could mean it IS just a display issue.
# Connect to a USB ammeter/multimeter. The amount of power the phone is consuming can tell you a lot. It is a way of getting a read on behavior based on
# Check with the old screen. It's possible the new screen is the issue. Or see if it powers on with no screen attached.
If it is truthfully not powering up, chances are the logic board was damaged during the repair. The battery remaining connected opens the possibility for circuits to be inadvertently bridged when power is running through them. This commonly happens when parts are connected or disconnected. Or if metal tools are used during the repair and it slips.