Sum depending on date range

Alright, after about 6 hours trying various formulae in Excel 2003, I've given up. I'm attaching the sanitized sheet. I need to sum the minutes in column E, within monthly date ranges. I've tried SUMPRODUCT, SUMIF, SUM(IF), IF, AND, VLOOKUP, and every other permutation I can find. When I use:

=SUMIF(A:A,"<=9/30/2008",E:E)

I get the proper answer of ":15" but if I try anything else, to denote the beginning date, as in

=SUMIF(A:A,"<=9/30/2008",E:E)+SUMIF(A:A,">=9/1/2008",E:E)

I get errors. I've tried so many things I've forgotten which errors go with which tries.

So, in column G, I'd like to be able to subtotal the accumulated time (from column E) since the last time it was billed (or maybe every month, or whenever). I can't just do a SUM and highlight the intervening rows in case a late entry with a past-date gets added, resulting in a fresh date sort, or is I'm asked how many hours I put in from [date] to [date].

It seems like it should be a simple search; it's been anything but. Advice?

Stephen