I mean, you don't forget your FRIENDS birthdays or ignore it! You do NOT have to be in love with someone to wish someone a Happy Birthday. This is obvious but you seem to miss this.
Well Ok, I forgot my friend's Bday last year.. Lots of stuff going on, I don't make notes of things, etc. I read it on her Twitter a few days later and apologized and she just laughed.
You're obsessed with her. Just because you want her as a friend doesn't mean she will be a good friend or wants to be your friend the same way. She wants you as a tool.