I have an online wallet
An online wallet is going to be either a hosted (shared) EWallet or a hybrid EWallet.
The hosted (shared) EWallet category includes Paytunia, Instawallet, Coinbase, exchange accounts (e.g., your BTC account at Mt. Gox, Bitfloor), or accounts with specific merchants (e.g., your BTC account with bitZino, bitMit.net, etc.).
None of these hosted wallets will provide you with the private key for your deposit addresses.
Another type of online wallet is a hybrid EWallet where you hold the private keys but the service is used for the spend transactions. Examples of hybrid EWallets are Blockchain.info/wallet and StrongCoin. You can see your private keys for your addresses in your hybrid EWallet, and transfer these keys elsewhere.
There are also mobile clients where the keys are stored on the mobile and not with a back-end host and the method of getting the private keys varies depending on the approach the mobile app uses.
Which type of service are you using, a hosted (shared) EWallet or a hybrid EWallet? (or, for more specific assistance, what EWallet service specifically are you referring to?)
I decoded the private key used by the online wallet and imported it into a new wallet in my software.
"Decoded"? Do you simply mean that you copied the private key (or exported it) from a hybrid EWallet (e.g., Blockchain.info/wallet) and then imported that key into the Bitcoin.org client?