PRODUCT IF - Multiple Criteria

I'm looking to multiple some numbers together if the numbers are within a certain time period e.g 2002 - 2008. I can create a PRODUCT(IF( function that will allow me to do this for a single criteria, however when I try using PRODUCT(IF(AND( with 2 criteria, then the product returns 0. Please see below for examples - ive picked a trivial second criteria which will obviously hold:

2001 1.018

2002 1.015

2003 1.031

2004 1.025

2005 1.032

2006 1.026

2007 1.045

2008 1.042

2009 1.000

2010 1.050

{=PRODUCT(IF(A1:A10>=2003,B1:B10))} = 1.279331 {=PRODUCT(IF(AND(A1:A10>=2003,A1:A10>=2002),B1:B10))} = 0

These answers should logically produce the same result as the second criteria trivially holds.

Any thoughts?