Matt,

Open the Bitcoin-QT client.

Wait for the blockchain to synchronize.

Go to your receive tab, copy the receiving address or the address that your coins were supposed to be sent to, we'll call this YourAddress.
Is it 1JJA3L6UGUtrK3MzscbKdWFt8mrv6eHfkk ?
If it is, then use that one.

Open up the debug console window, and type

dumpprivkey YourAddress

You should see the private key for that address. If it's not there, you don't have access to any coins at that address.