Coronary artery disease (CAD) is a common disorder that can lead to heart failure. Not all people with CAD are eligible for today's standard treatments. One new treatment approach uses stem cells—specialized cells capable of developing into other types of cells—to stimulate growth of new blood vessels for the heart. This study will determine the safety and effectiveness of withdrawing stem cells from someone's bone marrow and injecting those cells into the person's heart as a way of treating people with CAD and heart failure.