I am dealing with the same problem. Scanning many forums i have found upwards of six would-be solutions.
Some would include:
Updating your OS
Disabling any firewalls/make GW2 and exception
Run as administrator
The shortcut repair fix
Resetting modem/gateway
Changing your ports in DNS settings
Download an older client version
Sadly, all of the above (and then some) still yield no results for me.
After emailing support, somehow my client worked and i was able to play for about an hour (i just purchased two days ago)
Then a new build was released and i was asked to update to join a more populated instance. Of course my client would not update AGAIN. Back to the drawing board while i wait for support to review my game advisor report. Hopefully some of these methods can help some of you.