Our friend at AutoZone said we needed to fill the car up with gas, make sure we tightened the gas-cap, and the "check engine" light should go off in a day or so.
So we went to the nearest gas station. Filled up. Turned the car back on. No more annoying alerts on the dashboard.
It actually was that easy.
Price at AutoZone: the amount of money it took to put gas in the car
Price at the dealership: would have been $100, regardless of what they found
Listening to Sarah: priceless