Cell Match and Sum problem

Match 2 criteria in 2 separate columns of a Database and Sum up the respective values in a 3rd column?

I have a database table which extracts information from a legacy system in a fixed format. I would like to find a formula that matches criteria in 2 separate columns in the database table, and then proceeds to sum up the equivalent rows in the 3rd column.

I will apply the formula to build up a cross tab table which can then lend itself nicely to reporting and charting. Therefore a Pivot table solution is not appropriate in this case, and DSUM does not feel right as it requires a new criteria for every cell in the cross tab.

Any insights will be greatly appreciated.