I think you can be pretty certain the Xbox adapter is not faulty and you should keep it. Perhaps a Cheap wireless Access Point will serve better. You can buy a new one, but if you live in an urban area, buy one off craigslist. Be sure to search for the exact model number on craigslist because searching for 'wrt*' does not yield the results you want.
Also, a 5Ghz Access Point is recommended for reduced error correction in a densly populated area.
http://www.smallnetbuilder.com/content/view/30333/96/