I haven't actually had breakfast there, but I do know that one place that serves breakfast is the Pacific Wharf Cafe- they have scrambled eggs in a bread bowl, oatmeal, and I think pancakes (maybe). Not sure if any other places in DCA serve breakfast, but I'm sure you could get coffee and doughnuts at Baker's Field Bakery.
Also, one thing that I recently learned is that Steakhouse 55 at the Disneyland Hotel serves breakfast! Again, haven't tried it yet myself, but I've heard that it's pretty good and that it's priced reasonably.
I think b/c DCA opens later, the breakfast options are less. I was talking with the manager at Storyteller Cafe and he said that they get EXTREMELY busy between 9 and 10 because everyone hits the restaurant at the same time just before heading to the park. Hint: eat at Storyteller's cafe at 8:30 or 8:45 reservation. Also I agree with the Steakhouse 55 option as well, it isn't largely advertised but the breakfast is a good value and good food.
Tangaroa Terrace at the Disneyland Hotel also serves breakfast, and I think they open at 7 AM. And like John said, I think DCA opening so late is why there are so few actual breakfast choices in the park. By 10 AM most people are thinking about lunch.