It might be the fact that it's a PS2 you're trying it on. The Oddworld games are, like you said, very old. From the PS1 era. And eventhough Sony claims that all PS games are playable on the PS2, it might experience problems when you need to change discs. As far as I know the PS2 does not feature games that need to change discs anymore, so maybe that feature has been taken out of the console, which would explain why it doesn't grab onto it.
You can do two more things. See if you can rent the game somewhere, and see if it's the game discs. Or rent an old PS1 somewhere and see if it's the console. It has to be either one or the other. Let us know what how it evolved
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