I really do appreciate the help. It's nice to know that if I'm really in a crunch there are people who will take the time to help.
I resolved the problem with the following formula.

=SUMPRODUCT(--(LIST!D5:D314="Approved"),--(LIST!A5:A314>=LIST!K6),--(LIST!A5:A314<=LIST!K7))

It returned a 0 when I tried it with the date in the formula. When I put the start and end dates in cells and then refrenced the cells in the formula it worked. If anyone knows why the dates don't work in the formula I'd sure like to know.

I have never created a Pivot table before. I think I'll try that next.