Bitcoin-Qt frozen catching up/sync with Bitcoin in new wallet
If you still have the wallet.dat file from the bitcoin-qt installation at the time got the wallet address that you sent the money to you can use that with a new bitcoin-qt installation to try to make it work. If you don't have that wallet.dat file anymore the money is lost.

As for the problems downloading the blockchain, are you sure you have enough space? It's about 12 GB now. It sometimes take a very long time to download and may just look like it's sitting around for a while doing nothing, then pick up again a while later.