Recovery using a private key
If your private key looks like a proper Bitcoin private key, you can recover control over your money.
A private key is just a large number. There are several different ways of representing that number.
|Mini private key
(Don't use these values they are just examples)
Note the specific lengths and the specific mixtures of characters. I think WIF normally starts with a "5". Your private key needs to match these characteristics.
Wallet Import Format (WIF) is probably the most useful.
You should be able to choose a wallet and "import" or "sweep" your private key. Sweeping is considered safer because it works better with normal backups and recovery-phrases of the new wallet.
If you used Instawallet, it seems unlikely that you have a true private key.
Instawallet's service learned that its security was compromised and on April 3rd, 2013 closed the service. Those with funds in their Instawallet can file a claim form to get their funds.
This sort of issue is why custodial wallets are inadvisable for long term storage.