Do this when you are not able to connect to Ethernet but are able to connect to the Wi-Fi. Some common solutions for this problem of the Ethernet port not working are:
1. If one port is not able to make the connection then try connecting the laptop to different ports on the router.
2. If the cable is broken then the connection would not be secure. Try swapping the cable and test if the Ethernet is working.
3. If there are any Antivirus or Firewall then try turning them off temporarily so that nothing can stop you from connecting to the local network.
4. If the Ethernet is disabled then it would not work. Check this by
Press Windows + R keys together to open a Run dialog box.
Then type in devmgmt.msc and click OK to open the Device Manager.
Then expand Network adapters to find the Ethernet card device name.
In case the Ethernet is disabled then you would see a computer icon and an arrow.
Right-click the device name and then click Enable.
5. Finally, check whether the network card driver is working. Go to Device Manager > if a yellow exclamation mark is found next to the network device then update the driver. Find the driver in Asus website.