I tried another function to see what that would yield and it gave me exactly
the same answer as the sumproduct function.

I set up a column (AL in my spreadsheet) to count rows and placed the value
1 in each row. Cols E through H are the four terms that hold the codes I'm
looking for. I gave each array a name (N_M, N and M) as you suggested in your
first post.

Values is the name of the spreadsheet where the columns to count are
located, and this is the function I used:

=SUM(IF((ISNUMBER(MATCH(Values!E3:E2503,N_M,0)))*( ISNUMBER(MATCH(Values!F3:F2503,N_M,0)))*(Values!G3 :G2503=0)*(Values!H3:H2503=0),Values!AL3:AL2503))

Unfortunately, while it returns the same values as the sumproduct function,
the values do not equal those I get when I double check with autofilters.

Very, very confusing!