Can I retrieve my bitcoins from years ago that I never received? How can I get hold of my bitcoins that never made it to my wallet years ago? 

I purchased some bitcoins years ago (have got my receipt and all emails from who I purchased). I downloaded Bitcoin-Qt 7, synced it, got an address for the seller. It went through, but I could never sync it again as I was using prepaid internet credit. So, the bitcoins never got to my wallet! I gave up for a few years, but now I have unlimited download. Now Bitcoin-Qt 7 has a download issue. I switched to Bitcoin Core 11 now. I would like to know how I can get hold of my bitcoins?

Ther was no data transferred over to Bitcoin Core 11 sadly. Please can any one help me?
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