What is the exact model of your MBAir? You can get this information by clicking the Apple menu and selecting "About this Mac" or by entering your serial number here.
What version of macOS is currently installed?
Have you tried the SMC & PRAM resets?
Can you boot the laptop normally or in Safe Mode? If so, boot it normally and check the Network System Preferences to make sure the Ethernet is actually getting a valid IP address and you can get online using Ethernet. Ethernet should be the top network item in Network Preferences. You can also click the WiFi icon and turn off/disable WiFi to make sure you can get online using just Ethernet.