While traveling through Minnesota in the late-1990's I heard an old radio show rebroadcast of a sci-fi dramatization. It tells the story of bureaucracy gone horribly wrong, with the main proponent falsely charged for a minor infraction, but through delays, misinterpretations, obscure regulations, etc. he ends up being arrested, put in jail, and winding up on death row (for something akin to an unpaid parking ticket). I remember him desperately hoping for a governor's pardon shortly before his walk to the electric chair (but we know how bureaucracy works, don't we). The story was wry, pessimistic, but insightful about how bureaucracies work, and lasted only 10-20 minutes. However, I lost radio station reception before getting the title or author of the short story, or the name of the radio dramatization group who they were rebroadcasting. Anybody recall reading such a science fiction short story or hearing such a dramatization on the radio (probably done during the Golden Age of Radio Drama)?
Null has identified the written story that radio play was based on as "Computers Don't Argue" by Gordon R. Dickson, which was also the answer to this old question and this one. I'm adding this answer in an attempt to identify the radio play itself.
A "semi-dramatized" reading of "Computers Don't Argue", with musical accompaniment, was aired in 1978 on the program Mindwebs from WHA Radio in Madison, Wisconsin. If WHA rebroadcast that program in the late 1990s, you might have picked it up on your car radio while driving in southeastern Minnesota. You can listen to it at the Internet Archive.
The short story that the radio play was based on may be Gordon R. Dickson's Computers Don't Argue. A similar question was asked not too long ago, and this story was the answer to it. The story is written as a series of letters, many of which are generated by a computer or written by bureaucrats.
The original minor offense was for an overdue book payment, except it was a computer error. The "offender", a man named Walter Child, had ordered the book "Kim" by Rudyard Kipling but was instead sent the book "Kidnapped" by Robert Louis Stevenson. Mr. Child sent back "Kidnapping", asked for his copy of "Kim", and refused to pay the bill for "Kidnapping". The computer system used by the book club he ordered from continued to send him bills for the "Kidnapping" book and started escalating to a collection agency.
Eventually, through additional computer and bureaucratic errors, Mr. Child was accused of kidnapping and murder (for kidnapping Robert Louis Stevenson, who was presumed murdered as part of the kidnapping by the legal systems' computers). The computerized system also judged Mr. Child guilty, which landed him on death row.
There are mentions of attempts to get a last-minute pardon from the governor, which matches your description. For example:
As I was talking to Warden Magruder in my cell, here, news was brought to him that the Governor has at last returned for a while to Illinois, and will be in his office early tomorrow morning, Friday. So you will have time to get the pardon signed by him and delivered to the prison in time to stop my execution on Saturday.
The story ends with
the governor issuing a pardon for Mr. Child before Child is executed. However, the last letter is an automated notice of a "failure to route [the pardon] properly". The governor is instructed to resubmit the document on the Tuesday after Child's scheduled execution (the next day that the routing service is open). The notice also instructs the governor to submit a form with his supervisor's signature explaining his authority for submitting a document with a "TOP RUSH" category. The governor is threatened with arrest if he fails to submit the form, and is told there are no exceptions...
Could you be thinking of The Jigsaw Man, by Larry Niven?
In this story, a man escapes from prison and destroys an organ transplant facility after being sentenced to death for traffic violations.
Perhaps the classic The Trial by Franz Kafka? In this story a man is charged with an unspecified crime and put through a huge bureaucratic system over a long period of time. In the end, the man is executed.
The original story does not specify the original infraction, nor does it feature any sort of pardon from the governor (nor an electric chair), but those could have been added for a radio adaptation.
it probably isn't the right story, but I remember a Mark Twain science fiction story about an Austro-Hungarian inventor falsely condemned to death who finds proof (a television clip, I think) he is innocent but is executed anyway due to inflexible bureaucracy or something.
No doubt there have been many such stories vaguely similar to the once asked about.