I moved the wallet to Blockchain.info, it's not that I trust my gmail account (and dropbox) is completely safe now but I guess it must be impossible to enter the account after I put up the google key two factor authentication.
blockchain.info is even worse than a desktop client! You computer has been compromized. Moving to blockchain.info won't make things any better.
What you should do is backup essential documents, delete everything on your computer, reinstall the operating system, install anti-malware software like anti-virus apps and scan and restore the backups. Then change your passwords everywhere including your email accounts. As far as bitcoins go you should move all the coins to a new wallet. Make sure you set a password on your new wallet.