counting data ignoring certain cells

this is probably two questions in one-
I have a matrix table with two columns that need cell counting with criteria.
Basically one formula will ignore any rows that have blank cells or a zero quantity. It will also ignore duplicated Part Numbers if any. What should be left are non-duplicated unique parts having a quantity of 1,2,...etc(no zeros). The final count should be 13 which is really a cell count.

The second formula does exactly the same but instead of only counting 1,2,.. etc it will also count the zero quantities 0,1,2, etc. The final count will be 15 for that one I attached a spreadsheet with data and result table-if you wish to help. what formulas should i use?- please.

Thanks.