So you have at least one hardware issue with the logic board. Your keyboard backlight connector is broken, This is repairable, but you’ll need to find someone who has a junker to swap out the connector.
[image|2083852]
Your OS issue will need a bootable external drive to reformat and install a fresh copy of macOS. I would recommend sticking with Sierra. Here’s the needed image file & how to setup a bootable USB thumb drive:
* [https://support.apple.com/en-us/HT208202|How to upgrade to macOS Sierra], Jump down to Step 4 for the direct download URL
* [https://www.macworld.com/article/3092900/how-to-create-a-bootable-macos-sierra-installer-drive.html|How to create a bootable macOS Sierra installer drive]