There are good people in law enforcement who are capable of conducting an investigation of this sort. What's more they have powers to gather ISP logs and other information with a warrant to discover the identity of the culprit.
This is a sad tale but taking upon yourself (or expecting it from another) to investigate this type of incident may be counter-productive and potentially harmful. If evidence is tampered with e.g. unauthorised access to a mail account then the proper judicial process can be put at risk. Legal questions such as what laws have been broken arise and there's often not a good, tested answer at this time.
I share your feelings but this is not a road I suggest we go down. The only exception to this would be in the case of investigative journalism or a privately contracted investigator. Both should be aware of the law and how to conduct an investigation with a view to handing it over to law enforcement if need be.