Not really sure what's your set-up
(maybe you could post a sample in plain text?)
but here's another guess ..
Let's say you have
In Sheet1, in A2:E4
---------------
1111 3 0 1 7
2222 3 7 0 4
3333 0 8 5 9
etc
where 1111, 2222 etc in col A are product #s
In Sheet2
-------------------
Listed down in A2:A4 are the product #s
3333
2222
1111
etc
Put in B2:
=MIN(IF(Sheet1!$A$2:$A$100=A2,IF(Sheet1!$B$2:$E$100>0,Sheet1!$B$2:$E$100)))
Array-enter the formula (press CTRL+SHIFT+ENTER)
Copy B2 down to B4
You'll get the min non-zero values for each product in col B, viz:
3333 5
2222 3
1111 1
Adapt the ranges to suit ..