Try this formula
=SMALL((A1,C1,E1),INDEX(FREQUENCY((A1,C1,E1),0),1)+1)
Both SMALL and FREQUENCY functions accept "unions" as arguments, i.e. single cell references separated by commas and enclosed in brackets like (A1,C1,E1).
So the formula uses FREQUENCY and INDEX to find the number of zeroes in a range and if you add 1 to that you get the k value such that the kth smallest is always the minimum value excluding zero.
I'm assuming you don't have negative numbers.....