A common group of viruses that infect humans are enteroviruses. Enteroviruses produce illnesses in children which may range from very mild (summer colds) to severe (infections of the brain, liver, and heart). The purpose of this study is to determine if a new drug called pleconaril helps treat babies with enteroviral sepsis. In addition, researchers are attempting to determine a safe and effective dose of pleconaril to help babies with this disease. Infants who are 15 days or younger when diagnosed with enteroviral disease are eligible for this study. Two out of 3 babies will be randomly assigned to receive Pleconaril and the other one out of three will receive a placebo (inactive substitute). Participants will be hospitalized while receiving study medication. Babies will receive standard treatment care for their symptoms and will be observed for their medical progress. Participants may be in the study for up to 2 years.