Countif and Using WildCard

As Cutter states there are a few things that need clarifying.

You have more than one years data in your sample.
Does each year have to be calculated separately?

You have a number of negative values in "Gross" and you have a column for <= 300. Why?

Have a look at this workbook, I have added columns to both sheets, some might not be needed, but I have left in to help clarify the problems.

Select a year from the drop-down in Sheet "Form" A1

Hope this helps

Using your original sample file - my take on it would be to put a reference date corresponding to the Friday of whatever Week 1 would be in a cell - I have used Jan 8, 2010 in F1 as an example.

Then in B2 (and copied) down put this formula:
=COUNTIFS(Data!C:C,"<="&$F$1+(RIGHT(A2,LEN(A2)-5)-1)*7,Data!C:C,">"&$F$1+7*(RIGHT(A2,LEN(A2)-5)-2),Data!D:D,">300")

The references to the Week #'s in col A can be changed to ROWS() functions like this:
=COUNTIFS(Data!C:C,"<="&$F$1+(ROWS($2:2)-1)*7,Data!C:C,">"&$F$1+7*(ROWS($2:2)-2),Data!D:D,">300")

Try this workbook.

There are two possible solutions, one if you need the workbook to run on pre-2007 versions of Excel, "Form (2003)"
This uses SUMPRODUCT for the calculations.

If you are confident that the workbook will only need to run in 2007, or later, use "Form (2007)".
This uses COUNTIFS for the calculations and is much more economic on memory than SUMPRODUCT.

In both cases Columns I:J are for prooving purposes and can be deleted.

The department codes in sheet "Data" have a few anomalies e.g. 04 LA in some cases has extra spaces, and LA 04 seems to be at odds with the rest.
The formulae I have used allows for this and treats them as one code.

In Sheet "Data" column G seems to be redundant, all the values can be in column F.
I have combined these columns, but in case you need a visual check I have put a formula in column G.

With either "Form (2003)" or "Form (2007)"
1/. To change the year select from the drop-down in A1

2/. Column D is the grand total for each week in the chosen year.

3/. Columns E:G the headers are the search strings and the results are for each State for the chosen year.

4/. The drop-down in L1 might be a useful option, this allows you to count by State or individual departments, again for the selected year.
This might be where a problem could occur with the extra spaces in some of the codes.

Best to trim the codes at source, and decide whether 04 LA is the same department as LA 04.

Hope this helps.