 The purpose of this study is to determine whether a new medicine, called carvedilol, improves symptoms and heart function in children who have congestive heart failure diminished function of their heart muscle that pumps blood to the body. To accomplish this, we will give carvedilol to some patients who have diminished heart function and congestive heart failure and see whether symptoms and heart function are better at the end of an 8 month period in those who received carvedilol compared to the other patients who did not receive carvedilol. We will be testing 2 different doses of carvedilol compared to no additional medicine. 