Hi,
I would say you're trying to install a defective screen assembly, or it has been damaged by improper installation during your first attempt.
I would try a new screen assembly, making sure not to pull/damage the screen assembly flat cables.
But if you want to try your luck with a thorough troubleshoot, see the following:
1- Rule out dirty screen assembly connectors by cleaning them with a cotton swab dipped in 90%+ isopropyl alcohol. If the screen still doesn't work, move to (3).
2-a- Re the HOME BUTTON, look at step 31 of this guide. You will see 2 gold prongs. If they are missing, bent, or broken, go to (2-c). If intact, short them (touch them together with a metal tool to make them connect) and see if the home button function works.
2-b- If shorting them works, re-install the screen assembly and try the home button. If then it doesn't work, you have a bad/damaged home button flex cable that needs replacement using this guide for parts and how-to.
2-c- If shorting them doesn't work, you could (not very likely) have a damaged lightning connector assembly that needs replacement using this guide.
2-d- If shorting them doesn't work, you could also (more likely) have pry (did you remove or try to remove the battery? Did you touch the logic board anywhere next to the SIM slot and battery connector?) or drop damage that will need specialized tools and micro soldering skills to repair. Let us know, we'll help you out with your option in this case.
3-a- Your replacement screen assembly is probably defective or damaged. Try on a new one by following this guide and being specially careful and gentle around the flat cables that connect the assembly to the logic board. NOTE: if your old display assembly was broken but worked normally, put it back. If it still works like before, you know your new screen is defective.
3-b- If using a new KNOWN GOOD display assembly doesn't help, you probably have a logic board problem (drop damage or pry damage during your first repair attempt). If you reach this point, let us know and we'll guide you through more steps.