Most likely what you are seeing is that the phone is stuck on DFU mode. Screen light up but black screen. A program like 3UTools can tell you if the phone is in DFU mode.
Check the two screw holes near the screen connectors on the logic board for long screw damage.
It's the two lower screw holes out of the 3 upper right of the logic board that don't go through the board but on the board.
Use microscope to check for copper or exposed layers of the board in the screw hole.
If you see that instead of dirt / dust and a normal looking surface then it's unfortunately long screw damage which requires removing the short from the exposed / damaged layers of the PCB.
I can't really explain how to fix long screw damage as I have not done it before.
For that 2nd photo, what connector is that above or under? LCD display FPC connector or the Digitizer touch screen FPC connector on the logic board?
Could also be U2 Tristar charging ic issue, have you checked the rest of the board for liquid damage?
More info here: 5s wont boot up, error 4005
In this screenshot this is are the areas you touched up in green square:
Jumping that spot for backlight filter is okay, fixing up that trace for the LCD data lines is okay as well, I think those are not the cause of the stuck in DFU mode issue, it's something else.
How did the backlight filter go bad? Pry damage? Plugged in screen with battery plugged into board?