We are increasingly accumulating molecular data about a cell. The challenge is how to integrate them within a unified conceptual and computational framework enabling new discoveries. Hence, we propose a novel, data-driven concept of an integrated cell, iCell. Also, we introduce a computational prototype of an iCell, which integrates three omics, tissue-specific molecular interaction network types. We construct iCells of four cancers and the corresponding tissue controls and identify the most rewired genes in cancer. Many of them are of unknown function and cannot be identified as different in cancer in any specific molecular network. We biologically validate that they have a role in cancer by knockdown experiments followed by cell viability assays. We find additional support through Kaplan-Meier survival curves of thousands of patients. Finally, we extend this analysis to uncover pan-cancer genes. Our methodology is universal and enables integrative comparisons of diverse omics data over cells and tissues.