The easiest way I know is to do something of the form:
=SUM(IF(B1:B6<>"",IF(C1:C6="",1,0),0))
In this case, if the item in B is not blank, then one point is summed for each blank item in C; if C is not blank, then it's 0, if B is blank, it's 0. I didn't understand all the double negatives, so you would modify it to whatever combination of cells being blank or not blank you want.
It's an array formula (i.e. you hit ctrl-shift-enter after you type it in to make it work).