Using Sumproduct in place of CountIf

Hi! I have tried looking for a similar discussion on using Sumproduct in place of countif, but I can't find anything as simple as what I need! My countif function (yes, singular, countif!) just needs to count how many times a certain value comes up in this one column in an external workbook. Yesterday I learned the hard way that the IF stuff doesn't work if the external workbook is closed - BOO! - so, I need help!! I have tried reading up on how to use sumproduct and the information is just not getting through to my tiny brain. Can anyone help me?

Try

=SUMPRODUCT(--('\home\name\Excel\[Linker.xlsx]Sheet1'!$A$1:$A$12="A"))

Where "A" is your criteria. Of course, substitute your path.

It's easiest to set up the formulas with both workbooks open, then save the other book and the path will come up automatically.