"Unfortunately, you may have cause permanent damage to the unit by inverting screws.
You can take a look at the price of the 5s board right here and see if it suits your wallet :
iPhone 5s Logic Board
If you tried different cables, computers and itunes installation and you still have those messages, the issue is most likely to be linked to the hardware.
Last recommendation would be to manually download the ISPW file and Shift Click the restore button to select it and see if that kind of restore would work, but I really doubt it will.
Ok. So the majority of people are right. It definitely sounds like you've hurt your logic board, pretty bad. You can buy one from ifixit. THEYRE PRETTY GOOD THAT WAY. However, it's not you're only option. You can mail it to Jessa Jones. She's like a Demi-God. Or maybe even another repair shop like that. You can get your board repaired, and keep it, just the way it was
Probably it's "long screw damage" to logic board, typical damage when screw is put too deep and damage cooper tracks on logic board. Its possible to fix by soldering in jumpers to reconnect them back together, but its a job for a "pro". Check youtube , https://www.youtube.com/watch?v=TzlsG1M1...
