As per your description it seems that you are trying to give preference to Ethernet cable while keeping Wi-Fi enabled.You can enable Wi-Fi and cable connected at a time, but you can only use the Internet from one of them. The computer will prefer the cable if cable is connected.
If both are capable of providing Internet access, then computer will prefer the cable (Ethernet) network to access the Internet (and not use the Wi-Fi network to access the Internet).
The advantage of using two connections is to get Internet access without interruption when one connection does not work.
If your computer is picking up Wi-Fi right now then you can disconnect all connection and then try to connect first with Ethernet cable and then wirelessly.
Hope this would help. If issue still persists post back with current status of your computer and result of proposed suggestion, we will be happy to assist you.
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