Did you reccently do the "-image" trick to download all the game files? If so, your shortcut on your desktop will still have the "-image" command tag on it and won't actually start the game.
Right click, edit the short cut properties to return the command to normal.
Check that you are not using any programs that interfere with connections like peerguardian or something similar - they will also stop you from updating.
I know you checked your firewall, but if you're using NOD32 you need to take it off completely before it will connect to Anet. (From my experience at least; it does it after it updates sometimes.) Not sure if that's what you're using, but thought it's better to chime in just in case.