Yes, I restored the Ledger with the old PW's it seems and the new ones were lost.
Then if I understand your situation correctly, along with the 24 words you lost access to your coins. You need those 24 words, not any other. It's not a password that can be changed, it's a seed phrase from which private keys are calculated.
Also, will I still be able to obtain my Private key without my 24 PW's?
No.