I have a 2010 iMac running El Capitan and recently re-configured the network to use an ethernet cable connected to the back of an airport extreme router instead of running on a wireless connection. As mentioned above, I went to System Preferences, Network, and turned off Wi-Fi using the list of network connections on the left-hand side. I re-booted the system and made sure it came back up with only the Ethernet connection showing Green and Connected.
Good luck