Let's see...
The gas tank is filled with gasoline, correct? And the airtank you speak of is the source of air/oxygen for the intake of the engine. To make it simple we'll forget about the pressure of the tank or its capacity and disregard all the air-tite business and say this:
The ingine runs as usual but is doing so inside a perfect vacuum. It gets air from an air tank and gas from the gas tank. The battery is sealed, also.
The battery is the ony thing I could think of that is necessary for the engine to run that may be effected by the vacuum, but I took care of that by sealing it off. You just want to know what would happen if it ran in a vacuum. The engine would run fine; it has spark, gas, and oxygen. It makes sense to me that your vacuum would be short-lived because it would start to fill with whatever gases are expelled from the exhaust. By the way, I'm picturing the car sitting in a box-shaped room maybe as big as a house, though size wouldn't matter, with nothing else in it but the car. You could get more complicated, sure, but in the perfect scenario of vacuum room, car, gasoline, oxygen, and sealed battery the car should run fine and start pumping the once-vacuum full of exhaust immediately. Well, it'd run fine until Famine came along.