A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
=MIN(IF('Cleansed Data'!$I$1:$I$10000=Summary!$D$4,
IF('Cleansed Data'!$F$1:$F$10000<>"",'Cleansed Data'!$F$1:$F$10000)))
Note the use of a limited range like I1:I10000. Change 1 and/or 10000 to suit your needs.
With I:I, Excel creates an array with 1+ million elements, and it performs 1+ million sets of comparisons. That is very inefficient, if it is unnecessary. I suspect you do not have anything close to 1+ million rows of data.