Be hard to locate the problem if you hard wire it. When hard wired you pretty much bypass most of the stuff that could foul up your wireless signal. For instance you would not need to input any of the routers security information if you hard wired it.
So making sure you have security enable would be my first step (to avoid people from leaching off your wireless)
Second would be making sure the router is set up to use DHCP, and checking all security settings (writing them down)
Then I would be making sure i input all of the needed information into the Xbox correctly
SSID name, Type of security (WEP, WPA or whatever), TKIP or AES, and the security key (and passphrase is it has one)
It would surely narrow down why it isn't working and eliminate the most commonly missed parts.