The closest I can find to this is Hell is Forever by Alfred Bester, but while the ending is as you describe the rest of the story differs. The story was written in 1942 and has been regularly included in Anthologies since. I read it in Unknown Worlds Tales from Beyond, but that was published in 1988 so it's a bit later than your date.
The story is a novella rather than a short story. The protagonist Robert Peel fakes a demon summoning to scare his wife into dying of a heart attack. His wife does have a heart attack and die, but the summoning works and a demon is raised. This go rapidly downhill from there.
Peel does attempt to kill himself in a gas oven but the attempt fails:
When the room was sealed tight, Peel went to the stove, opened the oven door and turned the gas cock over. The gas hissed out of the jets, rank and yet cooling. Peel knelt and thrust his head into the oven, breathing with deep, even breaths. It would not, he knew, take very long. It would not be painful.
He came to with a start and realized that he had been kneeling before the oven for twenty minutes. There was something very much awry. He had not forgotten his chemistry and he knew that twenty minutes of illuminating gas should have been sufficient to make him lose consciousness. Perplexed, he got to his feet, rubbing his stiff knees. There was no time for analysis now. The pursuit would be on his neck at any moment.
He then tries several other methods of killing himself but they all fail. Eventually he uses a bomb that he makes himself by stuffing nitrocellulose from playing cards into a pipe. Then he heats the bomb over a spirit lamp and waits for it to explode.
With a sigh, he drew his desk chair close and hunched before the heating bomb. Nitrocellulose—a powerful-enough explosive when ignited under pressure. It was only a question of time, he knew, before the pipe would burst into violent explosion and scatter him around the room—scatter him in blessed death.
And it works:
There was a blinding explosion. It smashed into Peel’s face with a flaring white light and a burst of shattering sound. The entire study rocked and a portion of the wall fell away. A heavy shower of books rained down from the jolted shelves. Smoke and dust filled space with a dense cloud.
But as you say it leaves him blown into a thousand pieces but still alive:
And a thousand scattered bloody fragments of Robert Peel heard and understood. A thousand particles, each containing a tortured spark of life, heard the voice of Astaroth and understood.
“Of life I know nothing,” Astaroth cried out, “but death I do know—death and justice. I know that each living creature creates its own hell forevermore. What you are now, you have wrought with your own hands. Hear ye all, before I depart—if any of ye can deny this—if any one of you would argue this—if any one of you would cavil at the Justice of Astaroth—let him speak! Speak now!”
Through all the far reaches the voice echoed, and there was no answer.
A thousand pain-thomed particles of Robert Peel heard and made no answer.