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I decided to start reading some work of Lovecraft. 
Reading The Beast in the Cave,
I got stuck at the first paragraph I encountered:

The horrible conclusion which had been gradually obtruding itself upon my confused and reluctant mind was now an awful certainty. I was lost, completely, hopelessly lost in the vast and labyrinthine recesses of the Mammoth Cave. Turn as I might, in no direction could my straining vision seize on any object capable of serving as a guidepost to set me on the outward path. That nevermore should I behold the blessed light of day, or scan the pleasant hills and dales of the beautiful world outside, my reason could no longer entertain the slightest unbelief. Hope had departed. Yet, indoctrinated as I was by a life of philosophical study, I derived no small measure of satisfaction from my unimpassioned demeanour; for although I had frequently read of the wild frenzies into which were thrown the victims of similar situations, I experienced none of these, but stood quiet as soon as I clearly realised the loss of my bearings.

I think I managed to understand each separate clause,
but the logical relationships among them get me really confused.

I have no idea why the author used "yet", "for" and "but" at the places where I marked them in boldface. I also don't know why he wrote "my reason could no longer entertain the slightest unbelief", which means "my reason could not hold unbelief" if I'm not mistaken. Shouldn't he express something like "my reason could not hold belief"?

I'm feeling kind of frustrated now, could anyone help me figure it out?

Thanks to Greg Lee's answer, now I get a sense of what the author wants to convey. But I'm still not sure if I understand the exact function of these three words: "yet", "for" and "but". Is this "yet" related to "indoctrinated ... demeanour" (the sentence followed until semicolon) or "indoctrinated ... bearings" (the sentence followed until period)? Does this "for" stand for "because"? If so, I find this "because ... but ..." sentence structure really weird...

Yet makes an exception to the hopelessness: despite his grim fate, the narrator takes comfort in his lack of panic.

For introduces an explanation of why this would be comforting.

But contrasts what he did not do with what he did. A similar usage of but: “The Patagonian mara is not an ungulate but a rodent.”

These three conjunctions do not bear any special syntactic relation to each other; they're not like neither … nor, for example.

"my reason could no longer entertain the slightest unbelief" means "I could no longer doubt". He was convinced that he would never again see the light of day. He goes on to say that he was pleased with himself that he could accept this terrible turn of events with equanimity.

The prose style is deliberately impenetrable.

Hope had departed. 
Yet, ….

=

I had lost all hope, but I still had some pride
— I was proud of the fact that I wasn’t panicking.

…, I derived no small measure of satisfaction …;
for although I had frequently read ….

=

I was proud of my self-control because I didn’t panic,
even though (although) I knew that it was a common reaction
for people in similar situations.

…, I experienced none of these, but stood quiet
as soon as I clearly realised the loss of my bearings.

=

I didn’t panic, but rather I stood quiet.

Some would argue that the last sentence should say “I stood quietly …. 
I would agree that quietly would be acceptable here, maybe even preferable,
but I believe that the text is OK as is,
based on the following meaning of “stand”:

Oxford Dictionaries:

[no object, with complement] Be in a specified state or condition.
‘since mother's death the house had stood empty’
‘sorry, darling—I stand corrected’

American Heritage Dictionary:

To take up or maintain a specified position, altitude, or course:


• He stands on his earlier offer.


• We will stand firm.

Collins English Dictionary:

link verb

You can use stand instead of 'be'
when you are describing the present state or condition
of something or someone.
The alliance stands ready to do what is necessary. [VERB adjective]
He stands accused of destroying the party
in pursuit of his presidential ambitions. [VERB adjective]
The peace plan as it stands violates basic human rights. [VERB]

so “stood” essentially means something like “stayed”.