This study will examine the safety and effectiveness of treating adrenocortical cancer with combination chemotherapy using doxorubicin, vincristine, and etoposide in addition to the drugs mitotane and tariquidar and, when possible, surgery. Adrenocortical cancer cells have a large amount of a protein called P-glycoprotein that "pumps" anti-cancer drugs out of the cells, decreasing their effectiveness. Continuous infusions of doxorubicin, vincristine, and etoposide may improve chemotherapy results by blocking the P-glycoprotein pump, as may use of tariquidar, an experimental drug that is known to block the P-glycoprotein pump.