Ok so after doing some research about backwards compatiblity on the 360, I found one of my favorite games from the original Xbox, Yu-Gi-Oh The Dawn of Destiny, was backwards compatible. While I was very excited about this, I found a small game shop in town that actually had this game so I proceeded to buy it. Inspecting the CD before purchasing, there are no noticeable scratches, scuffs, etc... the disc is very clean, great! I proceeded to attempt to play the game on my 360, but no such luck. I have every single update on my console but the game still won't play. I have plenty of space on my memory cards and hard drive for any save files. Is there some type of hardware requirement for backwards compatibility to work correctly? Do only certain model Xbox or hard drives work for this? I'm about to go all "office space" on my xbox if I can't figure this out.
Edit:
Here is the exact error, took a shot with my camera phone:

