I'm pretty sure you can't play backed up xbox games without a modchip inside of the xbox, because I asked the same question you have asked, on another xbox modchip website.
Wrong you can get a softmod which dont use a modchip here is a tutorial on how to softmod... http://forums.afterdawn.com/thread_view.cfm/218495 HOW TO SOFTMOD XBOX EXPLAINED AGAIN FOR LAZY PEOPLE
Sorry about the bad reply, I read the question wrong, I thought you were asking about Xbox live, sorry my error.