Slow HR and 2 week notice

So I recently got a my dream job and couldn't be happier. I was told that HR would call within a week. Well more then 2 weeks later, I still haven't heard from them. I contacted the person who told me i got the position and was told HR was been slow and u should wait. The real problem in having is that I'm currently working and have to give 2 weeks notice. The program starts in two weeks . So my question is: should I give my 2 weeks notice if I still haven't be contacted by HR. Or risk waiting and not giving notice at my current job?
Don't give a notice until you have the job.