Hospital Energy Independence Act - Directs the Secretary of Energy (DOE) to establish a pilot program to award grants and loan guarantees to no more than six hospitals, including academic facilities that specialize in scientific research, provide patient care, and serve as health and medical education centers, during FY2011-FY2012 to carry out energy conservation projects for: (1) significantly improving energy efficiency; and (2) encouraging on-site power generation and energy storage, capable of operating independent of the grid, and providing sufficient on-site emergency backup power for essential hospital functions.