A PVT PLT invited a CFI to accompany the x-country flight because he was not instrument rated and marginal wx was forecast. On return trip from Atlanta the CFI filed an IFR flight plan. During the flight, the right fuel tank was run dry. Upon reaching the Chicago area, the flight was cleared direct Joliet, direct Dupage, and descend to 4000 ft. The PVT PLT stated the CFI relinquished control of the aircraft after stating, 'I have a severe case of vertigo.' PVT PLT stated he took control of the aircraft. Shortly thereafter, he requested a landing at Joliet because of low fuel. The flight was given radar vectors to Joliet after the PVT PLT stated he could not fly an instrument approach. ARTCC informed the flight they were 'right over the airport'; however, the PVT PLT stated they never located it. He continued that after descending to ground contact altitude, the engine quit and he began lining up to land on a highway at which time the CFI 'grabbed the yoke and put us into a steep turn to the left right into a grove of trees.' The CFI was fatally injured in the accident.