Sounds like you're just trying to do a classic two-column lookup. http://www.dailydoseofexcel.com/archives/2009/04/21/vlookup-on-two-columns/
Tons of solutions for this, most simple is probably the following (which doesn't require an array formula):
=SUMPRODUCT((Lookup!A:A=Param!A1)*(Lookup!B:B=Param!B1)*(Lookup!C:C))
To translate your specific example, you would use:
=SUMPRODUCT((A1:A3=A2)*(B1:B3="B")*(C1:C3))