If you want to record xbox 360 videos on your PC, you need a capture card. It doesn't matter whether your CD/DVD driver is screwed or not. The software can be downloaded from the Internet. Or you can ask your friend to copy software to a USB flash drive and install software from it.

There are also other ways to record your gameplays. You can do it with a video camera, DVD Recorder, VHS recorder, PVR,... connected to your gaming console (or to the output of your TV).

See also:
How to capture/record video from HDMI (record game play from XBox 360, PS3 to PC)

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