Seems like a case of hasn't cracked yet, not can't crack.
DNA is our best bet, but as we see it's the missing part of the story. With this said, it makes for a decent fictional writing prompt. It's 2045, the cold case on Mostly Harmless has been reopened after 24 years. Advances in DNA matching technology beyond what we imagined possible in 2020 have occurred. Detective Williams submits the preserved DNA to the US National DNA Registry (DNAR). Within minutes an exceptionall…
No, social networks are. More than likely there are people who absolutely know who he is, they just need to see the photo.
DNA databases are not necessarily comprehensive, if there aren't people in his lineage who are both registered and who know about/of him, then it won't work.