There are two main problems, or conflicts, in the story of "The Pit and the Pendulum."
The first conflict is a man vs. "something else" conflict. I don't feel comfortable saying that it's man vs. man, because the narrator isn't really fighting another human. It's not quite man vs. nature either, because he's in a man made environment (cell). It's also not quite man vs. supernatural, because he is fighting to survive against human torturers. So, man vs. something else it is. The narrator is fighting to save his life, or at least extend his life. The problem is that his torturers want the narrator dead. They want him to fall into a really deep pit, to be cut in half, or to be squished by burning hot walls.
The other main conflict is man vs. self. The narrator must battle with his own mental state in order to find the will to live. That's especially true at the end of the story, when he starts contemplating jumping into the pit to avoid the crushing hot walls.
Amid the thought of the fiery destruction that impended, the idea of the coolness of the well came over my soul like balm.