Need help! Initial sync not progressing, BTC sent already, + warning message
If you want to switch to Multibit, you can get the private key from the Bitcoin-Qt wallet using the debug console:  Help -> Debug Window -> Console.  Enter the command:

dumpprivkey public-address

This will list the private key associated with the public address you used to send the coins to your wallet.  You can then import this private key into a Multibit wallet by following this guide to import a private key into Multibit.

If you want to keep using Bitcoin-Qt, you can download the initial blockchain and then start Bitcoin-Qt to synchronize with the network.  Go here to download the initial blockchain.  Delete the 'blocks' and 'chainstate' folders in the bitcoin data directory and then unpack the downloaded file in the bitcoin data directory.  Start Bitcoin-Qt and it will rebuild the blockchain and then synchronize with the network.

The bitcoin data directory can be found here,