Average if between two dates...

Alright I've been screwing my brain with over thinking for the last couple hours. I'm gonna try and see if someone here can figure out what I'm missing..

Attached is a tiny excel file. It has two sheets. Sheet1 has a column (C) with dates ranging from 2/14/13 until 3/6/13. The next column (D) has random data next to it.

On Sheet2, I have two fields that call for start date and end date.

What I am looking for, it at all possible, is to set a cell value based on the average of the data between the cell start dates.

Example: If I set my start date to 2/21/13 and my end date to 2/27/13, I want a cell to return the average, which is 6.714286...

The formula I was working on looks like this:

=AVERAGEIFS(Sheet1!D4:D24,Sheet1!D4:D24,(VLOOKUP(E4,Sheet1!C4:D24,1,FALSE)>=E4),Sheet1!D4:D24,(VLOOKUP(E4,Sheet1!C4:D24,1,FALSE)<=E5))

It returns a DIV/0.

Anyone with an outside eye that can see what I'm doing wrong, which might just be everything?

Any help is appreciated.

I had about a whole 5% of it right.. Man I way over complicated this! Thank you so much! If you ever get to SE Michigan, you have a free drink on me.. Or a bag of candy... Or something... I don't really know but thanks!