I think the Matterhorn only has a 34" height requirement now, so if you child is willing, they can probably go on.
We took my son when he was 2 weeks shy of his 3rd birthday, and he had a blast. He didn't want to go on the Toontown coaster or the Matterhorn, and I didn't force the issue. He had a bad moment in the Haunted Mansion, before getting in the vehicles, but quickly calmed down with some reassurance.
He loved the fireworks, Peter Pan, Mr. Toad, Dumbo, the Parade of the Stars, the
Disneyland Railroad, the Mark Twain Riverboat, and Autopia (with some help of course), but his favorite was the Mad Tea Party. He road it three times (with no "extra" spinning).
As for DCA, they have a Carousel, and he loves the Electrical Parade. But there's not too much else. He went in the Animation attraction, but the only part he really enjoyed is the big lobby that shows the film clips. Blast wasn't there when we were there. There might be a Monsters Inc show (there was a few months ago, but not sure if its still there).
At that age though, the also just like to watch things like the Sun Wheel and Calfornia Screamin, listen to the music, and look at the lights.