I have plenty of questions:

1. Do you use HDMI connection?
2. What kind of video output have you tried on your xbox 360 (video resolution, NTSC or PAL)?
3. Do you get any picture in Media Express? What other software have you used?
4. What kind of motherboard do you have?
5. Can you record from other sources?
6. Have you tried to contact Blackmagic Design support?

Blackmagic Design Intensity Shuttle is very picky when it comes to video resolution and framerate. You will only see video Media Express or other capture software to the same resolution as is coming from your xbox 360. If your Xbox is using PAL instead of NTSC, then use 1080i50 instead of 1080i60.