If the issue disappears when you boot into recovery mode, then it is most likely a software issue. First try a full system update, and update all the apps. Try resetting all the phone’s settings back to their defaults. If this doesn’t work, you may have to disable all the apps one by one until the problem goes away in order to find the offending app.
The next step is to troubleshoot the video subsystem. First, look for an LCD cutoff switch or button on the laptop (some older models have this feature). The switch must be on for the LCD panel to work. Use the laptop’s brightness function keys to increase the screen’s brightness. If you added a graphics card to the laptop, make sure that the motherboard’s on-board GPU is disabled in BIOS/UEFI. Use a port on the laptop to connect to an external monitor. Use the display function keys on the laptop to toggle between the original monitor and the external monitor. If the external monitor works, then use in to go to Device Manager and update the video drivers. If this works, great, if not then replace the inverter, and then the LCD panel of the original monitor. If both the external monitor and the original monitor don’t work, then there is probably more than one problem with your system.
The problem is most likely the battery itself. Is this battery one that the manufacturer recommends? Apple can be a real stickler about what brands of batteries you can use in their products, and you may have to go to an Apple-authorized service location.
If the tablet’s display is misbehaving even when no buttons are being pressed, then please try a hard boot by removing the battery and reinserting it. Also, try a factory reset of the device to replace the software with a new configuration.
Based on the errors you are getting, the filesystem on the tablet’s hard drive appears to be corrupt. If the tablet is brand new, then you are in luck because you should be able to refund/exchange it. Please return it soon (hopefully you still have the receipt).
If the LAN port lights up, then it is functioning and does not need to be replaced. The next step would be to go to the PC’s Device Manager utility at devmgmt.msc and uninstall/re-install the drivers for the Ethernet adapter.
If you can connect to Facebook, then your Internet isn’t completely down. Try recycling the connection by turning Airplane Mode on, and then re-starting the internet connection. Also, please see if there are any system updates pending for your device.
If the issue started when the customer dropped their iPad, then the damage may be hardware-related. Reinstalling iOS may not help in this case, and fixing it might require actually opening up the device, if possible. Is the customer’s data backed up to iCloud (you may have already considered this)? Because if it is, it’s already safe. Please make sure that iTunes has been updated to its latest version. Error codes that appear when you try to connect to iTunes can sometimes be caused by security software on the computer blocking access to the external device. See if temporarily disabling any anti-malware programs doesn’t help.