If you are thinking of ORing the two criteria “HNT” and “HNT Fuel”, I am very much afraid that is not possible: OR doesn’t return anything of use to COUNTIFS. However, the COUNTIF and SUMIF formulas will accept an array of criteria, outputting an array of results, which you can sum up.
The following formula gets rid of the repetition and is extensible to allow for more variants:
=SUM(COUNTIFS('Sheet1'!$J:$J,{"HNT","HNT Fuel"},
'Sheet1'!$A:$A,"="&Q$4,
'Sheet1'!$AA:$AA,"<"&$A$2-2,
'Sheet1'!$AC:$AC,"="))
Note you do not need the = when comparing a string literal for equality (there are gotchas as to cell data to string conversion when you use a cell reference, but not with literals).
OR, but working nonetheless). – kopischke Oct 30 '11 at 15:41