This statement returns the correct result for records meeting these
conditions and dated before 11/8/2004:
=SUMPRODUCT(--($G$2:$G$2495="no")*($A$2:$A$2495="Colin
james")*($E$2:$E$2495<DATE(2004,11,8)))

This statement returns 0 for the number of records meeting the conditions
and dated between 11/8 and 11/12 inclusive. I know there are 23 such records.

=SUMPRODUCT(--($G$2:$G$2495="no")*($A$2:$A$2495="Colin
james")*($E$2:$E$2495=(2004/11/8))*($E$2:$E$2495<=(2004/11/12)))

What am I doing wrong?

thanks