Sending bitcoin from Bitcoin-QT v0.6.2.2 wallet
I don't know exactly what features are available on your version, but here are some ideas to try.

First, take a backup of your wallet.dat file.


In the debug window (help menu?), make sure that your peer is actually connected to some other peers so that your transaction will be broadcast to the network.
Make sure your node is fully synced to the latest block.
Start the application with the -zapwallettxes=1 argument to delete the transactions that are not in the blockchain from your wallet.
Start again with the -rescan argument to scan the blockchain for bitcoins assigned to your private keys. This will take a long time (hours possibly).
Your bitcoins should be available again, so try to send the transaction again with a higher fee. You can use https://bitcoinfees.earn.com/ to decide what an appropriate fee is.


If you really want to export your private keys, you can use the dumpprivkey "address" command from the console inside the debug window (if the console is available in your version). But be very careful when moving your private keys around, they could get stolen by a key logger, screen grabber, other malware, or phishing sites, etc.