It sounds like you have done everything there is to do. You emailed her instead of phoning regarding her birthday wish and after that was not received very well, you IM'd her. All that is left is smoke signals!

I agree with some of the other posts that your friend must have some more stuff going on that is allowing her to react like this. She knows you're sorry and she heard you crying on the phone and she can see that you keep trying to communicate with her so it seems like the ball is in her court.

I wouldn't beat yourself up about it. The first mistake made about calling her while she was busy isn't all that uncommon and happens so much with everybody. To continue to be this mad about it seems like there has to be more to her story.

I hope that things will get better and that you guys will be able to get back to being friends.