Also, if you have your private keys and you don't have the wallet address then the private keys remains useless so also when you have your wallet but looses your private keys.
The address is derived from the private key. So, the private key is all you need to have access to your coins
When you need to back up your wallet, you write down the wallet’s private keys (or seed in case of a HD wallet). You don’t need to write down the addresses as those can be derived from their respective PKs.
As you can see, OP has been able to recover his wallet and gain access to his coins (congratulations OP!) and all he had are the PKs.