Possibly your PC might have some trouble.
However, a Google search shows others connect to the Internt using wireless on the Xbox. Can you do that?
Reference:
http://www.overstock.com/guides/connecting-your-xbox-360-console-to-the-internetConnect your wireless network adapter. If your Xbox 360 console has built-in Wi-Fi, such as the Xbox 360 S, skip to the next step. Otherwise, snap the adapter into the tab slots on the back of the video game console and plug the USB cable into the port beneath. Extend the antenna. The green light on the adapter will turn on when it's working.
But the Wi-Fi adapter for the X Box is very privy and you are using sharing as an alternative. So let me offer two ideas.
A.) Go over you computer and look for any sign of malware or wrong settings.
B. ) Find a very low-cost alternative to the Xbox Wi-Fi adapter. I think you can get something for under $20 if you shop around.
But the major stores are charging way too much for this sort of thing.
I have found cheap Wi-Fi extenders for under $20 on eBay. An extender have serve as a bridge for Wi-Fi to Ethernet. Here is a typical item on eBay.
Click on the attachment to see a large view. I have bought two of the kind of such things from different vendors. Some have build-in antenna and work good. What you want is called a wireless client. It receives a signal and converts it to Ethernet.
(I rubbed out the sellers name. Many sell this product and different prices.)
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