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 :
[product|IF124-028]
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.
-Gl