I had the same problems - sound but no video.
My solution: Download the fixed exe (look for it here in this forum ...). Replace the original with the fixed one. Start the Game. Use Alt+Tab to go out of the game, then use Alt+Tab again to come back to Indiana Jones. Now you should see something! The goal is to get the Video menu and then change what in german is called "Erhöhte Grafiken", in english maybe "advanced graphics ?". However, you must choose "no" or "off" to turn the "advanced graphics" off. Then restart Indiana Jones and have fun with your son.
I just recently updated my son's PC to Windows 7 and got him the most of the Lego games also. Well when I go into IJ:Original Adventures I get a black screen, but I can hear the sound. His system is well above what is required to run it and the other games. I can also run Lego Star Wars, the Complete Saga with no issues. I put it on another computer and got the same black screen and the bad disk/authentic issue.
So is this an error that is caused by Windows 7 or is it a bad disk issue? I purchased two of these games from my local target this past week and only opened one so far. I don't want to open the other until I get this resolved.