If you have a bigger HD i.e. 120Gb you could dump your games via PXhdd loader and run them from the HD or rip them to the Pc and copy them back to the box manually. In order to do this you will have to have Evox installed with a modchip/bios capable of the Hd swap. Check out
www.xbox-scene.com for more info or check out some of the stickys on here.
There is know way at this present moment to copy a Xbox game via your Pc's dvd-rom, as the xbox uses a different file format. You have to ftp your pc to box to copy originals.