I have the EXACT same problem, I thought it was Alcohol 120% on my system, but after I removed that application, I still have the problem. The strange thing is, that one would think that the system would see the disc in the drive, but according to the system, there's nothing in the drive. I even plugged in an external DVD-CDRW drive and tried both 1394 and USB 2.0, the system still refused to acknowledge the disc. And I've never run that drive with this DVD before either. My internal drive is a Pioneer 110 DVDRW, my external is a TEAC. I ran a normal DVD to check to make sure the drive was still reading other DVD's, so I dropped in my girlfriends copy of Memoirs of Geisha, and it came up no problem.
It appears as though there is something on this disc that has been identified with the system not to recognize it. Did you guys have Alcohol 120% or some other Disc Image app on your systems? It leads me to believe that there may be some type of copy protection on the disc which is causing this error.
What baffles me is why would the game run 2 or 3 times and then fail?
Please keep this thread updated, I may have to contact EA tomorrow to see if I can get somewhere unless someone else has any ideas.