My Mac won't connect with Ethernet but will to wireless
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.