Below is a function I've somewhat put together. It is taking the Value of
shift "A" from column A, then, it's getting the month/year value from column
"B" and finally I am wanting to average the numeric values that meet the
criteria within columns "A" and "B" and averaging the values in column "D"
per month (month being: May-04, June-04, July-04, etc, etc). I am getting the
wrong value returned compared to a manual calculation. Where it is failing?

=SUMPRODUCT(('A Shift'!A4:A107="A")+('A Shift'!B4:B107="May-04")+AVERAGE('A
Shift'!D5:D107))

Here is sample of the raw data prior to pulling it together:
A May-04 Airwear 5384
A May-04 Airwear 5280
A May-04 Ovation 5379
A Jun-04 Airwear 4488
A Jun-04 Ovation 4553
A Jun-04 Ovation 4960
A Jun-04 Airwear(C) 4980
A Jun-04 Airwear 4037