Do any of you have any ideas on how I can play backup copies of my games on the xbox without using a mod chip?

I modified your post for legality reasons.

i'm moving this because it belongs in GAMEING not general. things dealing with games or consoles belongs in GAMEING...

http://www.xbox-scene.com/
should be everything u need...

You can do this easily, however once you do, you cannot use Xbox Live!

hmm depends what you do...
if you just softmod it you can still
drop to the original boot
i think thers only a prob if you get
a mod chip ~_~