I've been at it for more or less 2 hours, doing repairs, looking at fixes online, even did a clean boot of my computer. Origin will start normally, but if I try to run the game, it acts as if opening it, but then the "Play" button becomes clickable again and the game doesn't open.
I then tried the last thing I could do that was on the tutorials, removing the mods folder and trying to start up the game; it works and it opens normally. If I put back my mod folder, it goes back to not opening.

My game was working as usual until yesterday, I downloaded some CC hair for toddler Sims and some for adult Sims. I even checked most of the CC I downloaded yesterday, tried to remove them from the mods folder but the game wouldn't start up anyway.
Is there any way I can find out exactly which CC or mod is corrupting the game/preventing start up without having to check one by one?

https://www.patreon.com/posts/finding-broken-4-23751034

50/50? Test one half, see if the game starts, if it does, test the other half. Then part the problem half again, and test both parts, etc. Keep going until you've found the problem file.

Also make sure all mods and CC are updated to the latest patch and EP/SP/GP you have. Patches are notorious for renderingn CC incompatible, even seemingly harmless files.

Almost sure TS4 has cache files, which are known for causing bugs and can stop the game from running. Not sure exactly which ones can cause problems in TS4 (I play almost CC-free, so the caches haven't caused me any trouble yet), but in previous games they have absolutely been able to stop the game from running, so maybe check out this.

Thanks to the two of you for your help, I just found out what was causing the issue! It was a CC eyelash for toddlers that came with sliders (this one), the game is fine with the eyelash folder in there, but not the sliders folder. Since the eyelashes weren't appearing on CAS anyway, I just got rid of this one CC and could happily keep the others I had downloaded, thankfully!