There are a few areas of confusion in your post.
"There is no such thing as conjugation in Japanese"
I have no idea where you heard this, but this is simply not the case.
As one of my university professors often exhorted us, "define your terms." A lot of confusion can be avoided by starting from the terminology.
So, what is "conjugation"?
- Looking at Wikipedia's page for Conjugation, it's clear that we're talking here more specifically about grammatical conjugation. That article explains the word as:
In linguistics, conjugation (//ˌkɒndʒʊˈɡeɪʃən//) is the creation of derived forms of a verb from its principal parts by inflection (alteration of form according to rules of grammar). For instance, the verb break can be conjugated to form the words break, breaks, broke, broken and breaking.
- Japanese verbs definitely derive different forms by inflecting. For instance, the verb こわれる ("to break", intransitive) can be conjugated to form the words こわれる (plain non-past), こわれた (plain past), こわれて (plain conjunctive), こわれない (plain negative), こわれなかった (plain negative past), こわれさせる (plain causative), こわれられる (plain passive), こわれさせられる (plain causative passive), こわれさせられなくて (plain causative passive negative conjunctive), ... etc.
I can only think that whoever said that "there is no such thing as conjugation in Japanese" must be working from a different definition of "conjugation".
What is the derivation of the modern past-tense verb ending ~た?
My main source is the 日本国語大辞典【にほんこくごだいじてん】 (NKD), basically like the Oxford English Dictionary (OED) only for Japanese. Also, I am largely ignorant of the various Japanese dialects — I know they exist, but I do not know usage patterns, so the following is focused on mainstream 標準語【ひょうじゅんご】 or "media-standard Japanese".
With that said, let's go down the rabbit hole! 😄
The NKD entry for ~た explains that this arose as a contraction of ~たる, itself the 連体形【れんたいけい】 or attributive form of literary / classical verb ending ~たり. We first see this contracted ~た ending in the speech of the warrior class all the way back in the late 1200s or early 1300s in the 平家【へいけ】物語【ものがたり】 ("The Tale of the Heike").
Digging further into the derivation of ~たり, we learn from that entry that this is a contraction of verb ending ~て + copular ("to be") verb あり.
The ~て ending is often described in English as a conjunctive ending, since the basic meaning of constructions like [VERB1]
て[VERB2]
is often "[VERB1]
and then [VERB2]
". An example might be 「ご飯【はん】を食【た】べ[て]{●}、映画館【えいがかん】に行【い】く」 ("[I] eat my food, and then [I] go to the cinema"). Part of the intrinsic meaning in many of the uses of ~て come from its derivation, as the 連用形【れんようけい】 or continuative / adverbial form of completion auxiliary ~つ.
So ultimately, we have [VERB continuative / adverbial stem]
+ て (itself the continuative / adverbial of つ) + あり. The meaning could be analyzed as [VERB]
+ [completedness]
+ "is": the action of the verb is complete, and the resulting state is.
In modern Japanese, this is basically just the past tense: the action is done. From "do", to "did", etc.
- 食【た】べる → the "non-past" form. Basically, "[someone] eats", or "[someone] will eat".
- 食【た】べた → the "past" form. Basically, "[someone] ate", or "[someone] has eaten".
What is the grammar of ~たり?
The ~たり ending in Classical Japanese was both the 連用形【れんようけい】 ("continuative / adverbial form", used to modify another verb or possibly a whole verbal phrase) and the 終止形【しゅうしけい】 ("terminal / predicative form", used to end a sentence, and before specific auxiliaries that require a terminated clause), just as copular あり was both the 連用形【れんようけい】 and the 終止形【しゅうしけい】.
The ~たり ending persists in modern Japanese as the 連用形【れんようけい】, but as a kind of fossil, only used in certain constructions. More specifically, this appears when non-exhaustively listing a series of actions, basically saying "doing [VERB]
(and possibly other things too)".
For example, if asked what I did this weekend, I might say 「雑用【ざつよう】したり、両親【りょうしん】と電話【でんわ】したり、テレビゲームしたりしました。」 ("I did some chores, talked with my folks on the phone, and played some video games, among other things.") The ~たり~たり construction makes it clear that these are just some of the things I did.
What is the grammar of ~たる?
You'll see this attached to verbs pretty much only in Classical or very formal Japanese. In terms of meaning, this is the same basic past-tense as above. Grammatically, this is the 連体形【れんたいけい】 ("adnominal / attributive form") used to modify a noun or nominal phrase. This book about the Greek myths from 1935 (I think) contains an example (emphasis mine):
蓋【けだ】し冥府【めいふ】にて一【ひと】たび物【もの】食【た】べ[た]{●}[る]{●}ものは必【かなら】ず又【また】冥府【めいふ】に赴【おもむ】かざるべからざる法【ほう】あればなり。
This must be because there is a rule that anyone who has eaten something once in the land of the dead absolutely must return there.
A separate ~たる
There is a different ~たる suffix that you might find appended to nouns. This is a contraction of ~と + ある, and is basically the same thing you see in the so-called to-taru adjectives, words like 堂々【どうどう】 ("magnificent, regal, dignified"). The ~たる form is again the 連体形【れんたいけい】 or adnominal / attributive form used to modify a noun, so this must generally be followed by a noun or nominal phrase. The Digital Daijisen entry here includes a couple of examples. This is also from Classical Japanese, and has a very old-fashioned, formal, and stilted air to it, so don't use this in everyday conversation unless you like getting funny looks from people. 😄
Please comment if the above does not fully address your question, and I will do my best to update it accordingly.