This error could be an account setting in your PPPoE setup too.
More at http://ghost301tech.wordpress.com/2009/10/29/error-651-in-windows-7-a-killer-for-internet-connectionvpn/
Am just opening up my new computer, pre-installed with Windows 7 and have tried to connect via my existing wireless broadband connection, but get this Error 651 message. After a quick web-search (on old dying computer), I see someone suggests renaming a system file. But I am not upgrading from Vista, can't download anything on to the new computer (not online) and anyway am nervous about fiddling wih system files before I've even started. Any advice please? I can't really get much further with anything until I can get online...