It maybe just needs a reset, home buttons can be replaced they will just operate at a home button without finger print feature, I suggest replacing home button then you can reset it easily.
if that does not fix then next step is to look at hardware make sure all plugs are not damaged and plugged in correctly and flex cables of new screen are not damaged.
if still not joy it could be faulty screen try another , did your old screen light up try it and see if it still lights up.
next step is logic board damage maybe back light this will require micro soldering to fix.