If, as you say, you're absotively, posilutely sure the fault lies in the physical cartridge itself, then you have no alternative but to replace it.
But, I'd be danged sure there's no wiring errors in the arm itself. Disconnect the four wires from the cartridge pins and let 'em dangle without touching each other, get out your trusty VOM, and check the wires for shorts and continuity.
Make sure you respect the color code from the wires you disconnect.
Generally, it's:
Red = right hot
Green = right common
White - left hot
Black (or blue) = left common
Oh, there's also the possibility that the previous owner wired it for mono by jumpering the red/white terminals.
This, of course, assumes out any problems with the, phono, pre, or main amp.
[edit] Oh, you might find
THIS helpful.