My Mac won't connect with Ethernet but will to wireless
Solution 1:
the IP address came back as 169.254.122.206.
The 169.254.xxx.xxx address is a "self assigned address." It gets this address because it didn't get a DHCP lease from the DHCP server. This could be due to either of the following:
- No connection between your iMac and the router/switch
- DHCP server is down
Check your cabling from the back of the iMac all the way to the router. Make sure everything is plugged in properly. If you look at your Network Settings, it should be "green" and say "connected".
If it's yellow, that means it's plugged into a switch (getting power), but not communicating with anything. Check the settings on your router to be certain that the DHCP server is up and running.
Solution 2:
Here are the steps I followed to solve the issue on a Mac OS Cataline:
0-Start my mac without being connected to the lan.
Note: if I connect my mac to the lan and then I start my mac I do not have to do the below steps because it works fine and my mac gets connected.
1-Connect my lan cable to my mac
2-Go to system preferences -> network
3-Select my ethernet card that is not working despite the fact that my lan cable is connected (cf. image 1 below)

Remove this ethernet by clicking on the minus button (cf. image 2 below)

Select my bluetooth card (cf. image 3 below)

And click on the advance settings + select « renew the dhcp » + apply + ok to exit this window
Then click on the plus button to add a new ethernet interface (cf. image 4 below) 
Click on apply and the ethernet goes green to show that it is now connected. (cf. image 5 below)

The problem is not fully solved because I have to do these steps each time. It is not automatic. I need to find out how to make it automatic.