Bottom line: if it upset you that he didn't remember your birthday after you knew him for 2 weeks - move. on. girl. Because that's obviously a deal breaker for you. It's not going to get better.
Also, my fiancé never once tells me he's busy. Not even when he is. Sure, he doesn't answer the phone as fast anymore because we're getting married and he knows I like him, but if he had ever said "I was busy" as an excuse for not contacting me I'd say "too busy for me, bye!" and move oooon.
I did OKCupid (not where I met fiancé, sorry) and I can say this: don't be exclusive to one guy (especially for 2 weeks before even meeting!!) because NONE of them are giving you that same service. Try this: schedule a couple of "alright" dates for the week, the one you really want on the weekend, and then be completely honest about dating around. BUT don't put out to any of them because then they will assume you're doing that with everyone.
Once HE has asked you to be his exclusive girlfriend (and only accept those words) cancel all of your other dates and tell them why. If things don't work out with your new boyfriend, the guys will respect you more (and may consider you again in the future).
But don't be that serious about a new person knowing your birthday. If I were the guy, and I found that out, I'd run!