Like "Old Japanese" compared to Old English. I ask specifically Japanese because of the reduced contact to the outside world in the 1800s etc
Japanese has absolutely gone through language change. All languages have. Terms like "Old", "Middle", and the like are convenient, though not always accurate labels for different periods in the history of a language.
In terms of "Old Japanese" (abbv. OJ), historical linguists use that term to define Japanese as it was used before 794 CE, when the capital was moved from Nara to Heian-kyō (modern Kyōto).
Afterwards, we have Middle Japanese (MJ). Scholars do not all agree on when Middle Japanese ended and modern Japanese begins. Some, like Frellesvig (2010), put the end of Middle Japanese around the end of the Muromachi period, around 1573 CE. Others, like myself, prefer to call the start of the Muromachi period, 1336 CE, Early Modern Japanese. So we can already see that terms like "Old" and "Middle" are a bit hand-wavy and don't always get used identically (or rigorously; compare how a lot of people call Shakespeare's work "Old English", when it is really Early Modern English).
There are a number of linguistic changes that occurred--really finished--around this time.
One was the gradual shift from writing Japanese using man'yōgana (万葉仮名, so named because of its use in the oldest collection of vernacular (Old) Japanese poetry, the Man'yōshū) a script that used Chinese characters phonetically (that is, only for their sound value), much like how modern hiragana (平仮名) does. In fact, hiragana is just a limited set of man'yōgana written in cursive, which came into style in the Heian period in Japan.
There are also a number of sound changes that occurred/completed around this time. For a complete treatment, see Frellesvig 2010. Notably, Old Japanese had 8 vowels: /a/, /i/, /u/, /e/, /o/, /ə/, /ɨ/, and the diphthong /əi̯/. For convenience, I will transcribe these as a, i, u, e, o, ö, ï, and ë, respectively. If you are not familiar with the IPA, /a/ is much like modern Japanese a, and the same with /i/ and i, /e/ and e, /o/ and o, and /u/ and u (though the lips were perhaps rounded in Old Japanese). /ə/ is like the a in English about, /ɨ/ has no close equivalent in modern Japanese or English, but if you move your tongue from /u/ to /i/, it is about half way in between those two vowels. Check the Wikipedia article for a sample pronunciation. Finally, /əi̯/ is a dipthong---a single vowel that goes from [ə] to [i]. Canadians, and many other North American English speakers outside the South, have this as the diphthong in height.
Modern Japanese only has five vowels, /a/, /i/, /ɯ/ (like /u/ but the lips are not rounded), /e/, and /o/.
How do we know this despite not having recordings? Spelling. As I mentioned, OJ used man'yōgana. Later scholars, both in medieval Japan, as well as later in modern Japan and the West, found that some man'yōgana are only used to spell certain words. These words are spelled and pronounced the same in Middle and Modern Japanese, but not in Old Japanese. For example OJ pe (attested with the character 弊, which is never used to spell the syllable pë) 'side' != OJ pë 'bow (of a ship )' (attested with the character 倍, which is never used to spell the syllable pe). Likewise, yo 'night' != yö 'world'.
In terms of the country being closed, that seems to have had little effect on language change one way or the other. These changes progressed even in spite of Japanese using Middle Japanese as the de facto written standard language for quite some time (despite being quite unlike what people spoke, even among the upper crust in Kyōto and the various later capitals).
We in fact find that many of the "common sense" ideas about language change don't pan out under close scrutiny. For example, you might expect that with the radio, television, and the internet, American English speakers are becoming more like one another. In fact, we find exactly the opposite. Though some small dialects are getting swallowed up, the large regional trends are happy to continue on unimpeded. For example, the spread of the Northern Cities Vowel Shift has sucked up more and more lower and middle class speakers around the Great Lakes. Bill Labov, a sociolinguist, gave a nice interview about this a while back.
So tl;dr