The purpose of this study is to estimate the event-free survival (EFS) in children with stage I (non-pure fetal histology [PFH], non-small cell undifferentiated [SCU]) and stage II (non-SCU) hepatoblastoma treated with surgical resection followed by 2 cycles of cisplatin, fluorouracil, and vincristine sulfate (C5V); to determine the feasibility and toxicity of adding doxorubicin (doxorubicin hydrochloride) to the chemotherapy regimen of C5V for children with intermediate-risk hepatoblastoma; to estimate the response rate to vincristine (vincristine sulfate), irinotecan (irinotecan hydrochloride), and temsirolimus in previously untreated children with high-risk, metastatic hepatoblastoma; to determine whether timely (between diagnosis and end of second cycle of chemotherapy) consultation with a treatment center with surgical expertise in major pediatric liver resection and transplant can be achieved in 70% of patients with potentially unresectable hepatoblastoma; and to foster the collection of tumor tissue and biologic samples to facilitate translational research and to provide data that may aid in risk-adapted approaches for subsequent clinical trials.