Youre in luck, i actually managed to find the post.
Its not actually corrupted files; the animation plays fine in the preview window of the world editor (as you already wrote in your OP), and if you build these buildings in a custom map with certain triggers you will find that if you put the buildings animation speed to a negative value, the building animation will play from end to start just fine. Furthermore, if you reinstall the game, the bug will typically not go away. Its part of what makes this bug so odd.
I didnt find a solution to it online that actually worked, so i looked a little bit at the wc3 assembly back then. What happens is that for certain animations, the function that is supposed to reset the game time at which the animation started playing (the game uses this time to determine how long the animation has been playing and thus which frame is supposed to be displayed) was not called on certain animations. This resulted in that time value being in a default state which means that the animation either plays as if it started playing at the start of the game (e.g a building you start building after 30 seconds starts its birth animation 30 seconds in), or the default value was so far off that the animation started finished and wasnt shown at all.
Most notably, the function was called correctly if the building was started building outside of vision range, so if you scouted a computer building night elf or undead buildings, those worked just fine.
While i didnt find out why exactly this function wasnt called while looking at the game code (and to be fair, the actual solution is quite unintuitive), i have the luck to be playing a different RTS called Supreme Commander: Forged Alliance (the FAF version, to be exact), and over there, there is a relatively (compared to this bug, anyway) well known sound bug simply known as "the sound bug" that makes every sound in the game only play once until you restart the entire game, that also has the uncanny ability to persist even if you reinstall the game, and most strikingly, i noticed that even though i hadnt launched FAF in a while, after my warcraft 3 had that bug, FAF had its sound bug as well; and sure enough, after fixing the FAF sound bug, the warcraft 3 bug went away as well, which strongly suggests that these are the same bugs.
It sounds odd at first that its a sound bug that causes animation not to play, but if you think about what effects dont play (thunderclap, fire breath), you will notice that they all have sounds attached to them (though there are sfxs with sounds that play just fine, so the exact details seem to be a little complicated, but i didnt find an sfx without sound that was broken). In case of the buildings started outside of vision radius, the sounds dont play, so it makes sense that it works there. My guess is that the sound bug throws some sort of exception that ends up skipping the animation reset function, but gets caught earlier in the attach sfx to unit situation so there it still happens.
You can confirm this by disabling your sound device in the windows hardware manager and then playing the game. You will have no sound (obviously), but the animations should work again.
As for the solution that worked for me, i followed the steps in
this post. I don't understand enough about direct sound to know if there is an easier solution that doesnt require you to go into the god damned BIOS (or even understand how a global settings file can cause sounds to not play correctly), but it worked for me, and the bug is so rare that i havnt had it since. I heared from a warcraft streamer that had the bug around that same time that it fixed itself with the next windows update (which would explain why the bug just "goes away after some time"), so it might be easier to just wait for that, but dont quote me on that.