Stringing together formula in Excel to create one formula that looks at multiple factors

First off, your formulas and your TEXT do NOT agree.  For example:

If the value in D10=30 AND the value in E10='Days NET',  OR  the value in D10 is less than 30 (regardless of value in E10),  result is YES. 

I'm pretty sure is supposed to explain the first 3 equations:

=AND(D10>=1, D10<=31, E10="Days NET") – YES

or

=AND(D10<=30, E10="Days after receipt") – YES

or

=AND(D10<=30, E10="Days after EOM") – YES

BUT the equation says If D10 is between 0 and 32 (or 1 and 31 inclusive) and E10 is "Days NET"  OR D10 is less than 31 (or less than or equal to 30) and E10 is either "Days after receipt" or "Days after EOM" then result is YES.  This means if D10 is 31 (not 30) and "Days NET" , OR if D10<=30 then YES UNLESS D10 is 0 or less and "Days NET" then it would be NO.

So HansVogelaar​ gave a solution based on your equations but based on your TEXT I think you want:

=IF( OR(D10<30, AND(D10=30, E10="Days NET") ), "YES", "NO")

or alternatively:

=IF( (D10<30)+(D10=30)*(E10="Days NET"), "YES", "NO")