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I have not been successful in getting the following formula to work:
=COUNTIF(Matched,D2:F2)>0
Try the following method.
Define a name "Matched" and copy the following formula and paste into the "Refers to" field. (Concatenation of the ranges of 2 columns)
=Sheet2!$B$1:$B$100&Sheet2!$C$1:$C$100
Edit the ranges to be concatenated to incorporate sufficient rows of the 2 columns of data to search. However, do not try to contatenate the entire columns otherwise Excel takes too long to perform the required calculations when the Conditional format is applied.
Set the Condional format on On Sheet1 as follows:
Remove any Conditional format currently applied to the required range.
Select Range D2:D45 and hold the Ctrl and Select F2:F45. (so that you have 2 separate ranges selected.)
Open Conditional Format and use the following formula:
=AND(NOT($D2&$F2=""),NOT(ISERROR(VLOOKUP($D2&$F2,Matched,1,FALSE))))
Have tested this and appears to work fine provided that Named Concatenated range is not too large. However, the calculation time does not become a problem if in lieu of naming the concatenated range, you concatenate the 2 columns for the lookup into a speparate column and use that as the Table_Array in Vlookup. You could hide the column.