WOOOOOOOOOOOOOO I DID IT. Managed to fix it. It appears that even when BugMod is uninstalled, it makes some changes on the launcher that persist even when uninstalling the game. I deleted the Civ 4 folder in My Games, under my user's folder, and it managed to run! So there was indeed a conflict between 2 mods.
God, that was awful. I spent 2 entire days on this. I really thank you two for bringing me aid in this matter! If anyone else stumbles on the same issue I had and also seeks help making this run on their Steam version, just follow these 2 steps:
1. Make sure that no mod you've installed is messing with Civ 4's launcher. In my case, it was BugMod. Delete your mods folder (hope you have a backup of them somewhere) and delete the My Games folder on LocalDisk>Users>(User's name)> Documents>My Games>beyond the sword.
Make sure that you backup your savefiles if you don't want to lose them! Once that's done, verify game's files. Then proceed with step 2.
2. Unlike what the original installation instructions say,
DO NOT unzip the folder on the mods folder. For whatever reason, doing so creates an extra folder with the mod's name. Unzip it somewhere else, then cut and paste it to BtS mods folder. There should NOT be a "Ashes of Erebus" folder under another one with the similar name. This is what your installation should look like:
View attachment 555526
That's it! Have fun!