Excel 2007 : Sumif - inventory/running total

Have have been struggling to figure this out for some time...

I have

Part Arrival Dates (A2:A9)
Part Arrival Quantities (B2:B9)

Part Ship Dates (E2-F2)
Part Ship Quantities (D3 - G3)
Balance Left = (E4-F4).

I want to be able to enter all information and have the spreadsheet automatically calculate if I am shipping more product than is arriving between each arrival date.

So basically, Cell E4 would need to = E3 (-) anything in colum B2:B9 where the A2:A9 date falls between E2 and F2.

Then F4 would do the same thing but include that figure from E4, assuming there is inventory left.

Hope I didn't make that too confusing and i appreciate and all help! I have tried various "Sumif" formulas with no luck, so this isn't just an easy out for me!

I'm not sure how to do that w/o it pasting as simple text, so I've attached the spreadsheet i threw together quickly.

Thanks,
Chris B.