You are trying to see a head of department and they simply ignore your emails and phone calls, how do you go about this?

I would try to reach out to other physicians in the department and better understand the situation (personal emergency and so on). I will utilize my connections with other staff physician to get in touch with the director. If the matter is urgent and for example we need their signature on an application to be sent out, I will show up at their office or clinic and ask the reception for an urgent short meeting.