Could the man have died the same way in another confined area (say an elevator)?
No.
Does the fish have anything to do with HOW the man died?
Does the fish have anything to do with WHY the man died?
Did the man bleed to death?
Do you realize that if you’ve left and don’t keep playing this game until someone solves it, my entire afternoon is shot?
Yes. 
Was there a phone call involved before the man died?
Yes.
If so, did it have something to do with the fish?
Yes.
Does the fish have anything to do with HOW the man died?
yes.
Does the fish have anything to do with WHY the man died?
Yes.
The problem with these mysteries is that there are so many possible solutions.
Fer example, the man is carrying the package and drops it after spending his last dime (showing my age here) on the phone call.
Hopelessly wedged in, he starves to death after first attempting to smash his way out of the phone booth.
Or…he’s carrying fresh fish home in a newspaper when a pack of starving sabertoothed tigers observe him. He flees into the phonebooth for protection but it’s too late. He drops the fish in horror as huge talons of death rip through the glass and metal like they were tissue paper.
Or…a fisherman catches a prize fish and is calling home to gloat when a poorly operated forklift skewers the phone booth, knocking it off the dock into full fathoms five of water.
Or the guy with the fish is the 1-800-Call-ATT guy and he’s just finished another damn commercial when trained military SEALS finally locate him and pierce him with spear guns, leaving him thrashing in a final agony.
Did the man bleed to death?
Yes.
The plot thickens. Not unlike pea soup.
Did the man place the call?
Did the person on the other end induce the man’s death?
Was the fish completely dead? ARE YOU SURE?
Did the dead man initiate the phone call?
Did the broken glass kill the man?
Did he die from bleeding to death? (not exactly natural causes.)
did the man drop the fish and bump his head picking it up?
It’s never been specifically asked… Did the man break the glass?
~or was it something else?
~ someone else?
New and Improved
Enright3
So far:
Man dead in old-fashioned phone both, with two (opposite) sides damaged.
Nor murder or suicide or disease. Man broke glass while dying. Man has bled to death. Man was never trapped in the phone booth and did not break the glass for air. In another enclosed spot (such as elevator) man would not have died.
Raw, dead fish wrapped in newspaper at the man’s feet. Man brought fish into phone booth with him. Species of fish is irrelevant.
Phone call involving fish happened before man died.
Did the man place the call?
Yes.
Did the person on the other end induce the man’s death?
No.
Was the fish completely dead? ARE YOU SURE?
Yes.
Did the dead man initiate the phone call?
Yes.
Did the man get into an argument with the person he called?
Did the broken glass kill the man?
Yes.
did the man drop the fish and bump his head picking it up?
No.
Did the man break the glass?
Yes.
Did the man get into an argument with the person he called?
No.
Is WHO the man called relevant?
Did the man get the fish he was supposed to?
Would he have died had he gotten a different fish?
Does the size of the fish matter?
New and Improved
Enright3
Is WHO the man called relevant?
Somewhat.
Did the man break the glass by accident?
Finagle,
I think that’s what so fun about them. You’re given some obscure facts that could be just about anything, and you try to figure out what happened using only yes and no questions.
New and Improved
Enright3
OK, man is a diver. He leaned his speargun
against the outside of the phonebooth while
making his call. When slamming down the receiver, he accidentally jars the gun, setting it off and skewering himself.
Did the man ever end the conversation? ie: did he die mid-coversation?
Did the conversation cause him to become aggitated?
Did the man drop the fish before he died?
Did he call the person who sold him the fish?