The game loads fine, but whenever I make my teams and start a game (not online, just an "Exhibition" versus CPU), the game proceeds to that "spinning baseball" loading screen...and just stays there? The disc seems like it's spinning, but nothing happens.

Oddly enough, I've also got an ISO that I've tried - and it does the same thing!
I've also got NBA 2K & 2K2 and NFL 2K2 (also authentic GDIs) and they play just fine.