First,plug it into iTunes. See if it recognizes it,and if so,is it in recovery mode or does it show the general stuff…for example your name,storage left,songs on device,etc,or even a new device if you’ve never hooked it up to that specific laptop with iTunes.? This is the way to know if it’s powering on but only a display issue.
Second,did you unplug the battery prior to working on it? If not,here’s the thing. Even if the phone is powered off,some lines still have live voltage. Just open circuited. So if you snap the connector on so slightly crooked as it’s going on,it can short pins together and blow components. The backlight filter is very very very common to blow. It usually looks black and damaged,and the black over coating over it can look like it’s been burned off over one component specifically;the culprit.
3rd,you said after you put the bracket and screws on. Did you mix the screws? Or are you absolutely positive they went back in the correct holes? Long screw damage is a thing. Those holes have little silver rings the screws screw into. There’s no metal at the bottom of the hole. This means if the screw is too long,it will screw into the logic board and damage micro traces that lead to various components. If this happened,you’d have to send it out to be repaired by a microsolderer that repairs iPhones. The backlight filter is much easier to replace,but it’s something you can’t really do without a microscope and really good tools,costing hundreds,and lots of practice(LOTS),and knowledge.
4th,did you try unplugging the screen and plugging it back in(after unplugging the battery?)
let me know. I’ll try to help you out.