You need to first determine what the yellow stain is. A poultice may be needed to remove if it has been set for a while.
Since you mentioned your top is old, I imagine that it is a honed (not polished) finish. This is an easy fix. You can use sand paper to refinish. Start at a coarse grit that removes the scratches and work your way up to a fine grit. Stop at the grit that gives you the desired look. Use a white cleaning pad to smooth off the top. You will also want to use an impregnating stone sealer to protect your investment.