A jury in Alexandria convicted a Lynchburg, Va., teen-ager yesterday of attempted rape and first-degree murder in the strangulation of a 15-year-old girl. Gregory A. Joyner, 17, had told police in a a statement that he killed Sarah Jayne Jamison after she willingly had sex with him last May 15, then buried her body in a wooded area near her parents' home. Lynchburg Commonwealth's Attorney William Petty, who prosecuted the case, had sought a capital murder conviction against Joyner, which could have resulted in the death penalty. But lack of evidence of rape may have influenced the jury's convictions on lesser charges, Petty said. Joyner, who was 16 at the time of the slaying, faces possible life imprisonment on the murder conviction and a 10-year sentence for attempted rape. The defendant broke down in tears near the conclusion of the three-day trial, which was moved to Alexandria because of pretrial publicity in the Lynchburg area. Jamison's body was found two weeks after her disappearance, buried in a pile of leaves and debris. In his opening statement Monday, the prosecutor said police investigators and medical examiners were unable to find any physical evidence leading them to Jamison's killer because of the decomposed state of the body. Petty said the medical examiner determined by bruises on Jamison's body and its position that she probably had been raped. Petty said police were led to Joyner, a high school classmate of Jamison's, after reading an entry in Jamison's diary mentioning him.