Chinese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Chinese language. It only takes a minute to sign up.
Sign up to join this community
（1）刚来中国时，我一句汉语也没听懂。
（2）刚来中国时，我一句汉语也听不懂。
For me:
(1) states the situation that "I cannot understand Chinese sayings" without pointing out any reasons
(2) uses potential complement "听不懂" that means "I cannot understand" because not used to Chinese speaking speed or not know Chinese, etc...
Is what I think correct? If anything goes wrong, please let me know.
我一句汉语也没听懂: I may know some Chinese, but I don't understand what's been said.
我一句汉语也听不懂: I know nothing about Chinese, so I can't understand anything that's been said.
（1）刚来中国时，我一句汉语也没听懂。
（2）刚来中国时，我一句汉语也听不懂。
(2) is idiomatic, meaning when I just came to China, I don't understand a single word of Chinese.
(1) sounds odd in the context you made because 我一句汉语也没听懂 sounds like there were several languages being spoken and you didn't understand the Chinese language part.
For example, we have a discussion in which people used two languages, sometimes Chinese and sometimes English, and after the meeting you might say: (在会议里)我一句汉语也没听懂.
(1) 剛來中國時，我一句漢語也沒聽懂
When I first arrived in China, I wasn't even able to understand a word of Chinese.
This sentence is slightly unidiomatic when used by itself in Chinese, and would more commonly be used in a background context that's already understood. My immediate impression is that it would be the sentence which applies to someone who may have learned Chinese before, but wasn't accustomed to a normal-level of Chinese speaking speed, colloquialisms, accent, etc, and so wasn't able to understand anything upon arrival into China. For example,
雖然我已經在國外大學讀了三年漢語，但是，當我剛剛來到中國的時候，我一句話也沒有聽懂。
Even though I've studied Chinese for three years in an overseas university, upon my arrival into China, I wasn't even able to understand a word of Chinese.
(2) 剛來中國時，我一句漢語也聽不懂
When I first arrived in China, I didn't even understand a word of Chinese.
This sentence is usable as-is, but my immediate impression is that, without context, it implies that you never had any experience in learning or communicating in Chinese at all. For example,
當我剛剛來到中國的時候，我一句漢語也聽不懂。現在，在北京大學上完了一年的漢語課程之後，我新聞和連續劇都基本可以看得懂了。
Upon my arrival into China, I didn't even understand a word of Chinese. Now, after one year of attending Chinese classes at Peking University, I'm able to grasp most of what's being said on the news and TV dramas.
我一句汉语也没听懂
(I don't understand one or more than one of mandarin sentences through hearing.)
我一句汉语也听不懂
(I cannot understand even one mandarin sentence through hearing.)
这个在中文里不是一个大问题,我们平时是不在意这个的.
It's not an important problem, it don't count.
But!
举3个例子:
Here are 3 examples:
1=我懂了 I understood
2=没看懂(我每个字都认识,但是没看懂) I can recognize each of the characters, but I couldn't understand this sentence.
3=我不懂 I could not understand.
Despite these differences, we don't distinguish the two phrases strictly in normal life. Thus, there is no need for you to tell them apart.
（1）刚来中国时，我一句汉语也没听懂。 （2）刚来中国时，我一句汉语也听不懂。
It is literally a sentence, not a word.
If it were literally about not understanding a word, you would be seeing 一個字 or 一个字 in the sentence.
这两句话在汉语里没有什么区别，并不是像你所说的第一句未指明原因而第二句暗示了是因为不熟悉汉语的原因。事实上，第一句也暗示了说话者其实并不熟悉汉语，因为中国人表达听不懂的时候并不需要刻意强调听不懂汉语。
