core 2 duo has 2 core's you should be able to run the game fine since i can get 60+fps outside and inside constant 91fps on a PENTIUM D xD anways your crashing problem doesnt seem to be myour cpu or pc. try verifying your game files~?
EDIT: Misread? your board is intel C2D? but ur cpu inside ur case isnt c2d?? sry dont understand that english