Does my new iPad 3 have an audio input ...?
The new iPad, like all iPads, have a combined audio input/output jack, like the iPhone and newer MacBooks. The Genius was correct: Griffin cable should have worked. If it didn't, either the cable or the iPad was faulty.

One other possibility is that it was the software. This isn't very likely, but it's possible that the software you were using had some sort of compatibility issue with the new iPad.