Can I retrieve my bitcoins from years ago that I never received?
If you still have the wallet.dat file and your password you can access your bitcoins. You do not have to use Bitcoin-Qt 7 and it does not matter if your wallet ever synced before. If the sender sent the bitcoins to an address you control and the transaction was confirmed, the bitcoin are yours.

https://blockchain.info/wallet/import-wallet

If you want to use a new version of Bitcoin-Qt you can do that too: See Import wallet.dat into a new Bitcoin-Qt client