As someone relatively new to bitcoin, this means that my BTC is currently 'lost' so to say, un-received by the client but sent from my coinbase wallet. Is it possible to move the address (not the wallet because the BTC was never actually received right?) from the old hard drive to a new installation of bitcoin-qt on my new hard drive so that I can receive the coins?
Thanks for any answers ahead of time.
You don't "receive" Bitcoins in your actual wallet. Bitcoin-ownership is transferred to your address and a record of this is stored in the blockchain. Your wallet contains the private keys needed to access your Bitcoin-address. So the wallet-file is everything you need to access your coins. It does not matter if you had the entire blockchain downloaded or even if the machine with the wallet has ever been online. If the coins are in an address to which you have the private keys, you can access them.
So this means that you should recover your wallet.dat file and use it with another copy of Bitcoin-qt to send the coins. Or you could use a tool such as pywallet to extract the private keys from the wallet-file and import them in any other wallet-software (Multibit, Armory, etc...) or webwallet (Blockchain.info, etc...). This you can do today, or tomorrow or 5 years from now, it doesn't matter. As long as you have the intact private keys, you have the coins.