One reason might be to make sure they always have a web browser that works with their stuff. It wouldn't be beyond Microsoft's tactics for them to suddenly add some "feature" to IE that suddenly makes all of Google's Cool Stuff stop working well.

Also, if Google can promote adoption of Opera as a solid replacement for IE, the result will be that Microsoft's dominance is reduced. This is a Good Thing.

Why did they sign a contract that would not give them what they wanted.

To bad, they should have read it. They no longer have rights to the music the wrote and recorded, it belongs to Sony now