Diagnostics is always the way to go.
In this situation, I would first boot the phone into DFU mode to confirm that the phone can even power on. To do this, first connect your phone to your computer. Then hold the power and home button for 12 seconds. Then release the power button but keep pushing the home button. If your computer recognizes the iPhone in DFU mode, then the iPhone is still indeed functioning and the problem lays elsewhere. If not, then either damage to a vital component on the logic board has been ensued such as ESD damage (electrical static discharge) when disassembling the phone or the phone is not receiving any power from either the battery or an external power source.
Next, I would confirm that the work done on the screen replacement was done properly. I would check the flex cables and connectors themselves. Are they pinched or folded severely? Was the pin connectors damaged when trying to press the connectors back onto the sockets? I had actually damaged one of the very tiny gold tins in the connector of the 5S screen before and that has caused the screen to not function. Are the connectors properly seated and connected to the sockets? They usually snap into place on the sockets. When screwing the metal shield plating back over the connectors, did you properly torque the screws? Over tightening the screws can cause problems.
There are other methods i would go through before i come to the conclusion that the screen itself is defective. However, these are just the basic methods you should try first before deeming a screen as defective. Of course, if you receive your replacement screen after returning your defective screen to the vendor and the screen doesn't work, well the problem lies deeper into the logic board or you bought from a really crappy vendor that supplies low quality parts.
Best of luck