The fuel tank on these cars is in the trunk just behind the rear seat back not under the car. The fuel pump / filter is under the car, just in front of the left rear wheel ( there is a plastic cover over the pump / filter ) .

A burnt valve won't keep the engine from running. Did they say what cylinder has the burnt valve? If not they are probably just guessing.

We need more information, what is the history for the past year of this car?