After removing the home button, remove the two black rubber bumpers from the ‘Pentalobe Screw’ mount brackets and transfer them to the new screen, this helps secure the home button in place and screw tension.
Or anyone else reading this. I just replaced a shattered screen on iPhone 6+ and encountered the same issue. After some head banging I figured out that I had tightened the LCD ribbon plate too tight. After I adjusted all 5 screws to just barely snug, the phone powered on and functions with ought issue!