Update your graphics driver - if possible. That's simply a transparency drawing issue in the operating system (splash screens are just transparent windows of sorts).
Thanks! I did check on the driver, and it is up-to-date. The larger question for me, though, is why specifically Illustrator does this and none of the other apps in the suite. I have only had this issue with Illustrator in both CS5 and CS6.
Has no one else encountered this issue? It may just as I'd feared! Haha. Like I said, all of the other Adobe products have normal splash screens, so I don't think a driver issue really makes sense. Why would it only be affecting Illustrator and not Photoshop, Dreamweaver, etc? I really hope I don't have to just chuck my computer off a bridge. Any other feedback would be much appreciated!