Notwithstanding part 1 of this chapter, or any other provision of law governing post-conviction relief to the contrary, a person convicted of and sentenced for the commission of first degree murder, second degree murder, aggravated rape, rape, aggravated sexual battery or rape of a child, the attempted commission of any of these offenses, any lesser included offense of these offenses, or, at the direction of the trial judge, any other offense, may at any time, file a petition requesting the forensic DNA analysis of any evidence that is in the possession or control of the prosecution, law enforcement, laboratory, or court, and that is related to the investigation or prosecution that resulted in the judgment of conviction and that may contain biological evidence.