Punch Parker appeared in the first two issues of World's Finest Comics. He appears to be a private detective, as he is called in after a medical firm has a shipment of radium stolen, but no other information is given about this character.
Punch tracks the stolen radium to Suburbia, which seems to actually be the name of a town in this tale. Mad scientist Dr. Pear had the radium stolen for his elixir of life. Parker retrieves the radium, but the fight starts a fire that kill the mad doctor.
Punch Parker's second, and last, case is far more exotic than the first, dealing with murderous plants. It starts as a relatively simple investigation into a poisoning, but winds up pitting the hero against semi-sentient flora.
The killer, who has wound up working for a foreign government because of his gambling debts, winds up perishing at the hands of his own hybrid plants. Parker burns down the greenhouse a the end of the story.
As this was his final tale, I suspect that, although he seems fine, he was also poisoned by the plants, and died shortly afterwards.