Count Unique instances across several Columns

Try this, with CTRL+SHIFT+ENTER, rather than just ENTER

=SUM(IF(FREQUENCY(IF(C$2:C$53=Equip,IF((E$2:E$53>=StartDate)*(E$2:E$53<=EndDate),IF(F$2:F$53<>"",MATCH(E$2:E$53&"|"&F$2:F$53,E$2:E$53&"|"&F$2:F$53,0)))),ROW(F$2:F$53)-ROW(F$2)+1),1))

Of Course should have more intellectual ways.

Change the Equipment, Start & End Dates.