Use, with appropriately adjusted paths,

=SUMPRODUCT(('C:\Users\bob\Downloads\[closed wb.xls]closed'!$A$2:$A$3=$A4)
*('C:\Users\bob\Downloads\[closed wb.xls]closed'!$C$1:$D$2=B$3)
*('C:\Users\bob\Downloads\[closed wb.xls]closed'!$B$2:$B$3>=$B$1)
*('C:\Users\bob\Downloads\[closed wb.xls]closed'!$B$2:$B$3<=$C$1)
*'C:\Users\bob\Downloads\[closed wb.xls]closed'!$C$2:$D$3)