He ran back to the lower storey and tried the door. It would not move. He ran up again, and sweat began to trickle down his face. He felt that even minutes were precious, but one by one they escaped; and he could do nothing. He cared no longer for Shagrat or Snaga or any other orc that was ever spawned. He longed only for his master, for one sight of his face or one touch of his hand.
At last, weary and feeling finally defeated, he sat on a step below the level of the passage-floor and bowed his head into his hands. It was quiet, horribly quiet. The torch, that was already burning low when he arrived, sputtered and went out; and he felt the darkness cover him like a tide. And then softly, to his own surprise, there at the vain end of his long journey and his grief, moved by what thought in his heart he could not tell, Sam began to sing.

His voice sounded thin and quavering in the cold dark tower: the voice of a forlorn and weary hobbit that no listening orc could possibly mistake for the clear song of an Elven-lord. He murmured old childish tunes out of the Shire, and snatches of Mr. Bilbo’s rhymes that came into his mind like fleeting glimpses of the country of his home. And then suddenly new strength rose in him, and his voice rang out, while words of his own came unbidden to fit the simple tune.

In western lands beneath the Sun

the flowers may rise in Spring...

Going from:
‘King’s man! King’s man!’ his heart cried within him. ‘You must stay by him. As a father you shall be to me, you said.’ But his will made no answer, and his body shook. He dared not open his eyes or look up.

To:
Pity filled his heart and great wonder, and suddenly the slow-kindled courage of his race awoke. He clenched his hand. She should not die, so fair, so desperate! At least she should not die alone, unaided.

The characters are often bewildered and they're bewildered in two senses. They're bewildered because they're lost in wilder land, they don't know where they are. Sometimes of course, they discuss where they are. Mary and Pippin are particularly lost because they're too idle ever to look at a map. But even Aragorn has a good idea where everything is, he is often lost in the sense of not being sure what to do. So they're bewildered in being lost in wilder land, but they're also bewildered in they don't know what to do. Aragorn in particular feels this strongly I think at the start of book two, because he has to make a string of decisions. Okay, Mary and Pippin have been carried off. Frodo and Sam have gone off in the other direction. Who's he gonna follow? Mary and Pippin, they've been taken by Orcs...
A lot of it is an effect of the complex separations which take place. Like I say, first movie road movie. Second movie, second book characters are going off in all directions. Frodo and Sam, Mary and Pippin, Aragorn, Legolas and Gimli. Gandalf comes in, they swap over then Pippin goes off with Gandalf. Mary goes off with the riders or goes off with Éowyn. The characters are zipping backwards and forwards all the time. Gandalf sort of criss-crossing...

And why does he [Tolkien in his books] have this complex net of criss-crossings and bewilderments and speculations? Well I'd say the answer to that, is fairly clear. What he's saying is, and I can sum it up in four words, which is the old motto of the British Red Coat. Which is, "Look to your front." You don't look to the sides, don't look to see what your mates are doing. You don't need to know that, cause if you're looking to see what they're doing. They'll be looking to see what you're doing. And you will have frightened each other in no time. Certainly don't look behind you, look to your front. Or another way that it's put and this time it's Gandalf's words. Gandalf talking to Frodo early on in the book and repeated twice actually by Jackson.

He says, "All we have to decide is what to do with the time that is given us". All we have to do is decide what we're going to do. Do not think about other people. Once you start making your decisions on the basis of what you think other peoples decisions will be, you are speculating. And when you start speculating, you will inevitably get it wrong. You will actually frighten yourself, and drive yourself to wrong conclusions. Like Denethor and indeed like Sauron. Well, I think actually in the book all that's quite clear. It's a statement about the way events are in the real world. It's telling you what is the right procedure in the real world. But in the movies, it's quite different... .

‘I am glad that you are here with me,’ said Frodo. ‘Here at the end of all things, Sam.’

‘Yes, I am with you, Master,’ said Sam, laying Frodo’s wounded hand gently to his breast. ‘And you’re with me. And the journey’s finished. But after coming all that way I don’t want to give up yet. It’s not like me, somehow, if you understand.’

‘Maybe not, Sam,’ said Frodo; ‘but it’s like things are in the world. Hopes fail. An end comes. We have only a little time to wait now. We are lost in ruin and downfall, and there is no escape.’

‘Well, Master, we could at least go further from this dangerous place here, from this Crack of Doom, if that’s its name. Now couldn’t we? Come, Mr. Frodo, let’s go down the path at any rate!’

‘Very well, Sam. If you wish to go, I’ll come,’ said Frodo;...Frodo and Sam could go no further. Their last strength of mind and body was swiftly ebbing. They had reached a low ashen hill piled at the Mountain’s foot; but from it there was no more escape.

But even while he spoke so, to keep fear away until the very last, his eyes still strayed north, north into the eye of the wind, to where the sky far off was clear, as the cold blast, rising to a gale, drove back the darkness and the ruin of the clouds.
...
two small dark figures, forlorn, hand in hand upon a little hill, while the world shook under them, and gasped, and rivers of fire drew near. And even as he espied them and came swooping down, he saw them fall, worn out, or choked with fumes and heat, or stricken down by despair at last, hiding their eyes from death.

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For Merry, I'm not entirely sure whether he was in despair/without hope, or whether he wasn't really thinking in those terms at all and everything was simply immediate, and full of choices, without really much room for him to know if he was feeling despair or not.

Good insight, Ethel. While he was in conflict, he didn't have the luxury to weigh all his options or engage in much introspection:

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I'm trying to think my way through Merry's feelings and actions, but he did no such thing: he was a blur of instincts and principles and fear and inspired courage, all very immediate as you point out, and he just acted on a very hasty plan and on whatever emotions took hold of him. I do think that overall, Merry was determined to do what was right, even if he was in a situation for over his head.