Squeezing more conditions into a sample SUMPRODUCT formula - show a novice pls!

Hi Wizards!

I have the following formula:

=SUMPRODUCT((NINOSyNINAS!D4:D5000="F")*(((NINOSyNINAS!GA4:GA5000<=TPRIII!A11)*(NINOSyNINAS!GA4:GA5000>=TPRIII!A10))+((NINOSyNINAS!GB4:GB5000<=TPRIII!A11)*(NINOSyNINAS!GB4:GB5000>=TPRIII!A10))))

What I would need to do is to add the following condition to this formula:

Only count IF

NINOSyNINAS!BP5:BP5000 OR
NINOSyNINAS!BQ5:BQ5000 OR
NINOSyNINAS!BR5:BR5000 OR
NINOSyNINAS!DG5:DG5000 OR
NINOSyNINAS!DH5:DH5000 OR
NINOSyNINAS!DI5:DI5000 OR
NINOSyNINAS!EX5:EX5000 OR
NINOSyNINAS!EY5:EY5000 OR
NINOSyNINAS!EZ5:EZ5000 OR

is not blank.

I figured the new condition would look like this:

((NINOSyNINAS!BP:BP5000<>"")+(NINOSyNINAS!BQ:BQ5000<>"")+(NINOSyNINAS!DG:DG5000<>"")+(NINOSyNINAS!DH:DH5000<>"")+(NINOSyNINAS!DI:DI5000<>"")+(NINOSyNINAS!EX:EX5000<>"")+(NINOSyNINAS!EY:EY5000<>"")+(NINOSyNINAS!EZ:EZ5000<>""))

But how do I fit it in the main formula?

I tried:

=SUMPRODUCT((NINOSyNINAS!D4:D5000="F")*(((NINOSyNINAS!GA4:GA5000<=TPRIII!A11)*(NINOSyNINAS!GA4:GA5000>=TPRIII!A10))+((NINOSyNINAS!GB4:GB5000<=TPRIII!A11)*(NINOSyNINAS!GB4:GB5000>=TPRIII!A10))))*((NINOSyNINAS!BP:BP5000<>"")+(NINOSyNINAS!BQ:BQ5000<>"")+(NINOSyNINAS!DG:DG5000<>"")+(NINOSyNINAS!DH:DH5000<>"")+(NINOSyNINAS!DI:DI5000<>"")+(NINOSyNINAS!EX:EX5000<>"")+(NINOSyNINAS!EY:EY5000<>"")+(NINOSyNINAS!EZ:EZ5000<>""))

But it does not work...

Thank you for your help!!!