you should just get the router because they charge about a dollar per foot for the ethernet cable. You should just buy the Xbox wireless adapter in Ebay. Thats where i got mine.
You can buy a 100ft ethernet cable at either Radio Shack, Wal-Mart, Target, or K-mart. They shouldn't be that expensive and it should work on Xbox Live.
i only have $150 and i planned to buy membership and a game along with the ethernet cable. so i cant buy the adapter
You can order one off of amazon. Also some Gamestop stores have them. Haven't checked lately though.
You should be able to find it at Amazon
Try your local GameStop or Computer Store.