Replaced display screen but phone won't turn on?

Okay so I replaced the original screen that was factory with the phone as it was broken and cracked, yes before I replaced the screen it worked and after i replaced the screen it worked as I previously said I turned it off after seeing that the display powered on and finished putting the phone (home button etc) together. As I also previously said the device was recognized by my computer but I was unable to enter my passcode as my screen won't work.

And no I haven't checked it with another battery as I don't have one.

Does the old screen still work? Try that one.

Also you didn't mix up the screws for the metal plate that goes on top of the screen connector cables on the logic board right?

As putting the longer screw where it shouldn't be can damage the board circuit traces and cause no backlight / no display.

I tried the old screen and it didn't work, I put them in the right order but I fear I may have screwed them too tight, I have since loosened them and I think rehousing the home button may have done damage too :/ Is there any way I can salvage what's on the phone?

If I've stuffed the logic board will replacing that with another new screen work? and If I replace the logic board do I lose everything? Thank you so much for your help so far ben!