Your syntax looks wrong (though it is legal). The first parameter for
COUNTIF is the range, and the second is the criterion. [Look it up in Excel
help.]
You have asked it to count how many cells in the specfiied range meet the
criterion. The range you have specified is the one cell $D4, and the
criterion is that the value in the cell be equal to the minimum of the range
$D$4 to $D$15. You'd therefore get an answer of 0 or 1 from your count.
You'd get the same answer from
=IF($D4=MIN($D$4:$D$15),1,0) or from =--($D4=MIN($D$4:$D$15))
What are you really trying to calculate, where do you want zeros ignored,
and do you realise that conditional Formatting (which you mention in the
subject line) affects only the display, not the underlying value in the
cell?