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Default Can a date range be used in SUMPRODUCT

I have a Check Register Budgeting project. I want to total all of the checks
that cleared within a particular month for a particular accout. Each check
is recorded on a separate row so that Register!B4:B90 is the range that
contains the date the check cleared, Register!I4:I90 contains the
account/budget ID, and Register!D4:D90 contains the amount the check was
written for that I want to total.
This is what I have tried so far to total only one date (01/15/2008):

=SUMPRODUCT(--(Register!B4:B9=DATE(2008,01,15)),--(Register!I4:I9=G5),Register!D4:D9)

The formula above works, but when I try to replace the first array with a
date range like this it blow up:

=SUMPRODUCT(--(DATE(2007,12,31) < Register!B4:B90 <
DATE(2008,02,01)),--(Register!I4:I90="ACCOUNT#1"),Register!D4:D90)

Any suggestions?
 
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