Countif bringing back Value Error.

I am by no means an expert but I have been using formulas for the last couple of years, and either I am attempting to conquer this while my blood sugar is low or I am missing something entirely. I have one range that would be populated with "as needed" dates, or blank spots. I want to only count the dates IF they *1 are not blank *2 a different range has a "Y" in the cell AND*3 if a third range has a "C1" in the cell. My formula looks as such:
=COUNTIFS(F4:S55,"*",E4:E55,"C1",B4:B55,"Y"). This is by no means my first or 20th attempt at this. After reading forum after forum I have attempted this using many sum/count/if(and functions and I am at the point I have forgotten which all methods I have tried. Now I am reaching out...where am I going wrong on this? Thank you in advance!

yes, the larger range is the range needed to count. Each column corresponds to a document and the date within a cell corresponds to a training date. This range is what I need counted BUT only if the other ranges fit my criteria.

If the larger range is what is failing my function.... should I break range up to fit, or is there a better function for my needs?

I am wanting cells populated with dates and with "as needed". Only blank cells will not be counted, provided the other criteria are met as well.

THANK YOU!!!!!!!!!!!!!!!! I have been working on this for 4 hours.... I would have never used sumproduct!

I just re counted, it's coming up with a much larger number than what is accurate

I have attached 2 jpg files using the manage attachments option, so let me know if nothing shows. The actual file was too big to load, even with me extracting only 2 sheets and deleting all of the charts. Pic 1 shows the range in which the criteria are being met or not. If any of the cells in B4:B19 are "Y" AND any of the cells in E4:E19 are "C1" then count ALL non blank cells (dates greater than the corresponding dates in row 1, and "as needed"), in the corresponding rows of the criteria, within range "F4:T19". The formula would be in "AZ3" (shown in the second image) as crew 1 completed. All of the cells that aren't date inputs are formulas extracting it from other pages. If this is of no use and there is a way I can get the actual file to you let me know.

I figured as much.... but the file is too big. Any suggestions?