It sounds like the only way to retrieve the bitcoins that are at the addresses stored in my wallet.dat file is to get Bitcoin-QT working again.
No, as i said if you export the private keys you can move them to another client. You can for example use blockchain.info webwallet, just drag and drop there wallet.dat (note: learn how blockchain.info works before doing this)
It fails when "verifying database intergrity", but what database?
The blockchain (note: do not confuse with the website blockchain.info
)that the qt client have to download.
I don't know why it doesn't work, sorry