Try this:
=SUMPRODUCT(--(Sheet1!A1:A10="ABCD"),--(Sheet1!H1:H10="Dummy"),--(ISNUMBER(Sheet1!I1:I10)),--(Sheet1!I1:I10>0))
If column I will contain only numbers or empty cells then you can eliminate
the ISNUMBER test.
=SUMPRODUCT(--(Sheet1!A1:A10="ABCD"),--(Sheet1!H1:H10="Dummy"),--(Sheet1!I1:I10>0))