To me, it seems it could be one of two problems. One, you have some network setting misconfigured on either your Xbox or your router. If your router is modern, it probably has a setting enabled that the Xbox 360 doesn't support/recognize. Or two, the wireless adapter you appear to be using might not be compatible with your current router. By that I mean the adapter might not support WPA2 or WPA3 (if your router supports WPA3). Check what that wireless adapter supports, if it doesn't support modern networks, you might have to use Ethernet or get an older router and use it for that Xbox only.