2006 Honda Ridgeline Engine breakdown

We recently took our truck, a Honda Ridgeline, into a shop for transmission problems. We have been told that the transmission, as well as the radiator both need replaced. The radiator evidently leaked into the transmission. After a $2,600 quote, we had another call from the same shop informing us that the engine was now also shot. Apparently carbon monoxide is to blame for ruining the engine. We are now looking at a total of $6,000 in repairs. Oddly enough, the shop recommended not doing it for the time/money wouldn't be worth it. What would you suggest we do next? Is it possible for carbon monoxide to ruin the engine?