The bitcoin-qt client has a command called dumpprivkey that can export your private keys.
launch your bitcoin client as usual and wait for it to load the blockchain and start up
click on 'help' in the menu bar (top right)
click on 'debug window'
select the 'console' tab
type: walletpassphrase "your walletpassphrase here" 600
type: dumpprivkey [your public key here]
this will return the private key, you can copy it now; ensure you clear your clipboard/history afterwards
type: walletlock
walletpassphrase and walletlock is only needed if your wallet is encrypted.
If you are unable to start bitcoin-qt you can dump the private keys with pywallet to back them up.
The issue your having looks like the blockchain may be corrupted. You can try starting the client with -reindex but this will force the client to redownload the block chain. This will take a long long time. atleaste it did for me.