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What is a word to describe the situation in which there is no alternative or something cannot be helped?
I am looking for a neutral word, similar to impotent, instead of the slightly negative helpless, grudgingly, willy-nilly or nolens volens.
For example, how do we describe this situation?
The teacher's lecture is dull, but I have to sit there and listen. I have no choice.
In Japan the (-.-) icon is used in text messaging and in Chinese 無奈 is used to describe this.
Hummm...you might be looking for inevitable:
Adjective: Certain to happen; unavoidable: war was inevitable.
Noun: A situation that is unavoidable.
Synonyms: unavoidable - inescapable - ineluctable - necessary
I get the impression that you're looking for the English equivalent of what in Japanese would be termed shikatanai (仕方ない).
This phrase is usually translated as "it can't be helped" or simply as "unavoidable". Since you are looking for just one word I would suggest unavoidable, which has a neutral connotations, or its synonym inevitable.
Note, however, that translations of shikatanai into English are very context dependent. In the example sentence you used (The teacher's lecture is dull, but I have to sit there and listen. I have no choice) I would not use "unavoidable" or "inevitable". In fact, in that sentence I think a case could be made for saying that the word "have" already implies that it is unavoidable. If you would want to emphasize the "shikatanai-ness" of that specific situation I would simply write it as "The teacher's lecture is dull but I have to sit there and listen. It can't be helped."
Not a very satisfying answer, I know, but I do believe it is accurate to say that there is simply no one word in English that can be applied to as broad a spectrum of situations as the Chinese 无奈 or the Japanese 仕方ない. It really does depend heavily on the context.
Your example,
I have to sit there and listen. I have no choice.
can be rewritten with must or compelled; e.g.
I must sit there and listen. I have no choice.
I am compelled to sit there and listen. I have no choice.
By the way, another word to add to your "not like" list might be volitionless, lacking volition, volition being "mental power or ability of choosing; the will." For example,
Volitionless, I'm compelled to sit and listen.
Maybe you're looking for the notion of "binding", which is at the same time means imperative/compulsory and limiting/constraining.
"I'm (feeling) bound to sit here till it's over, can't help it."
You can use it like "a binding situation" as well. Bounden is also a word, as in "My bounden duty." Of similar meaning is incumbency.
And then there is impendency, as in impending doom, which is something also bound to happen but in the close future--like the words fated, fateful and fixed.
Maybe not the best possible example, but I am perforce moved to write this...
perforce - by necessity; by force of circumstance
In OP's example, The teacher's lecture is dull, but I must perforce sit there and listen.
I think it's fair to say that perforce is at the very least formal, and some might say it's becoming dated. I'm not sure exactly how informal willy-nilly is, or how much the original willing or not meaning has been supplanted by the later sense of haphazard, but it's certainly still current.
I suggest constrained over perforce. Constrained does not carry the specific connotation of force. It simply means limited by circumstances.
You are not as clear as you could be, but I have a feeling that you are looking for the antonym of alternative.
This is necessity.
Necessity is neutral in the sense of reluctance (it is used for things you try to avoid and for things you wish for).
You might describe yourself as being subject to (or subjected to) something (e.g., your teacher's lecture).
