The present invention improves corn dry milling in several ways. Integrated corn biorefinery processes are disclosed which can produce ethanol, edible corn oil, DDGS, solvent-extracted meal, power, and optionally crude corn oil, starting from corn. Some variations employ corn fractionation and edible corn oil recovery using liquid carbon dioxide, avoiding hazardous hydrocarbon-based solvents to produce edible corn oil. Some variations employ integration of gas-fired co-generation into the dry-milled corn ethanol plant to significantly reduce energy usage and carbon footprint associated with the overall process. Counter-current drying is preferably employed to produce a high-quality DDGS product with high protein content, low mycotoxin content, and low residual ethanol content.