Here is the formula you need, this is an array formula so you have to finish it off by pressing Ctrl + Shift + Enter.
=SUM(IF($C$2:$C$1700=0,1,0))
To check for additional conditions such as blanks just add nested IFs like so:
=SUM(IF($C$2:$C$1700=0,1,IF($C$2:$C$1700="",1,0)))