You'd make life easier for yourself and pb71 if you don't type the dollar signs in col D, which makes them text (you can instead format those cells to have dollar signs).

Then the formula in I2 becomes

=MIN(IF(( $A$2:$A$7=$G$2) * ($C$2:$C$7=$H$2), $D$2:$D$7))

... which still must be confirmed with Ctrl+Shift+Enter.