Problem with Countifs with 3 criteria (one being date)

Problem.jpgI just joined the forum so I am not sure where to post this problem. I have been trying to create a countifs formula with 3 criteria (that includes date in "mmm-yy" custom format as one of the criteria & text in rest) but it is not working. By the way there are blanks in the sheet too. The date range is along a row while the text ranges are along columns of the sheet. The formula which I tried initially is as follows;

=COUNTIFS(PI!$K$1:$CP$1,$A3,PI!$G$3:$G$201,F$37,PI!$H$3:$H$201,$B3)

I tried both with and without array but none works. I even tried extending the criteria range of the date to $HD$1 but still it is not working and giving me #value!.

I even tried variation of SUMPRODUCT but they are either giving value error or wrong results. Some of the Sumproduct syntax I tried are

a) If(SUMPRODUCT(--(PI!$K$1:$CP$1=$A3),--(PI!$G$3:$G$201=F$37),-- (PI!$H$3:$H$201=),COUNTA(PI!$G$3:$G$201=F$37),"")

b) SUMPRODUCT((IF(ISblank(PI!$K$1:$CP$1=$A3),0,PI!$K$1:$CP$1)=$A3)*(IF(ISblank(PI!$G$3:$G$201),0,PI!$G$3:$G$201)=F$37)*(IF(ISblank(PI!$H$3:$H$201),0,PI!$H$3:$H$201)=$B3))

c) SUMPRODUCT((MOD(row(PI!$K$1:$CP$1),6)=0)*(PI!$K$1:$CP$1=$A3))*SUMPRODUCT($G$3:$G$201=F$37)*(PI!$H$3:$H$201=$B3))

I have browsed extensively for last 2 days but unable to get a solution for this... I am attaching a screenshot of the sheet .....Please help.

...... Sorry the upload did not happen properly... now I am uploading both the screenshot as well as the sample xls file (in zip format due to size) which is similar to my original file. In the xls file, the BEFORE sheet is Prod_Support and the AFTER sheet is Summary sheet..... I am trying to count ONSITE & OFFSHORE TEAM SIZE using the criteria of Month, Project Type and Location...... Hope this information helps in getting a solution......

screen shots are pointless and anyway i cant see one in your post
Attach a sample workbook. Make sure there is just enough data to make it clear what is needed. Include a BEFORE sheet and an AFTER sheet in the workbook if needed to show the process you're trying to complete or automate. Make sure your desired results are demonstrated, mock them up manually if needed. Remember to desensitize the data.

Click on GO ADVANCED and use the paperclip icon to open the upload window.

View Pic