Your intended configuration lacks enough specific detail.
I agree with Congo, and would add that you might try running ipconfig /all to make sure the Xbox is "seen" on the system it's hardwired to first. Then note the mac address. If you can't pull up an IP on the Xbox, chances are good that you won't be able to add it to the network.
If you get a good IP from the Xbox, (depending on your wireless router brand and setup), the mac address might have to be added to the mac address filtering table in the router to allow network access as a peripheral device. At least, this has worked for me on a couple of occasions with non standard devices. Router make, model, OS type information would be helpful too.
Good luck
Mick

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