Could it be the timing belt? The car has over 143,000 miles

At that mileage, the belt should have been replaced once already. I can't find information as to whether the engines are interference engines which will have bent valves, but regardless, if the timing belt is broken, you'll feel puffs of air spitting back into the air filter housing when a helper cranks the engine. You might also be able to look inside the valve cover after removing the oil cap to see if any rocker arms or camshafts are moving. If they are, the belt still could have jumped a few teeth and not be completely broken.