What can I do if my vocal cords don't make a sound due to heart disease?

There are two general causes of the problem you describe, but both are related to the laryngeal recurrent nerve being affected. One is that the enlarged heart compresses the recurrent laryngeal nerve, resulting in hoarseness, and the other is that the recurrent laryngeal nerve is mistakenly injured during surgery. If the heart function improves after surgery and the heart shrinks, the pressure on the recurrent laryngeal nerve is relieved and the hoarseness improves. There is generally not much that can be done about nerve damage after surgery, and the normal vocal cords on the opposite side will partially compensate for the function of the damaged side.