Conclusion, I need to open the wallet.dat file with the good Bitcoin Core client... And I can't find it

Did you try extracting the addresses/wallets in it? I saw you can open it with a simple text editor or using a tool that do that automatically, there are existing (but be careful choosing/using a tool, it can be harming)!
Do Bitcoin Core don't gave you the list of your wallets ?

You can just check the balances manually!