Old Wallet, Private key and known public address
Your wallet will contain a collection of private keys, and it should show you the balance of the addresses associated with those keys.

For the public address you mentioned, if you have the private key associated with it, you'll be able to spend the coins. If not, there is no way to recover a private key from a public key. The private key is either known by the wallet file, or not. There is no way to 'resend' a payment, etc, to recover a private key that is otherwise not known.