The screws near the battery connector pass through the board to mounts on the housing of the phone so I don’t think you have damaged the board there as another post mentions.
If you haven’t yet, try booting the phone without the battery and without the front camera assembly. A damaged front camera can throw up some weird errors if it was damaged during the repair. It’s a long shot but a heck of a lot better than the next fault i’m about to mention. . .
If you got the screws mixed up when putting the shield over the screen connections, you may have long screw damaged the board there. With the screen removed and the charge port facing your body, check the bottom right screw hole for the screen connection shield. If a long screw has been screwed into that hole you may have destroyed a connection path in one of the boards layers. Not an easy repair, but a reputable shop should be able to help in this case.
How to resolve bootloop problem (long screw damage) iPhone 5s
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