Civil War Sesquicentennial Commission Act - Establishes a Civil War Sesquicentennial Commission to plan, develop, and carry out programs and activities appropriate to commemorate the sesquicentennial of the Civil War.Requires the Commission to award a grant in each of FY 2004 through 2016 to: (1) the U.S. Civil War Center at Louisiana State University, Louisiana; and (2) the Civil War Institute at Gettysburg College, Pennsylvania.