1. Go to the 'Start' menu and click on the 'Control Panel' item. Click on the 'View network status and tasks' link. Click on the 'Set up a new connection or network' link to create a new connection. Select 'Connect to the Internet,' select 'Yes, I'll use an existing connection' and select your PPPoE connection from the list. Re-enter your username and password, select the 'Anyone who uses this computer' option and click on the 'Connect' button. This might solve your problem. If you still see the error 651, try other solutions.
2. Go to the 'Start' menu and click on the 'Control Panel' item. Select 'Internet Options' and go to the 'Connections' tab. Place a check mark in the 'Never dial a connection' box. Click on the 'Apply' button to save your changes and then on the 'OK' button to close the 'Internet Options' window.

3. Open your Web browser and navigate to windowsreference.com/wp-content/uploads/2009/05/raspppoe.zip to download a fresh copy of the Windows Vista 'raspppoe.sys' file. This file commonly causes an error 651 in Windows 7. Note that the 'raspppoe.sys' file from Vista works in Windows 7. Save the file on your hard disk.
4. Go to the 'Start' menu and click on the 'Computer' entry to open the file browser. Navigate to the 'c:\windows\system32\drivers' folder. Select the 'raspppoe.sys' file, press the 'Shift' and 'Delete' keys at the same time to delete the file. Click on 'Yes' when asked if you want to permanently delete the file.
5. Right-click on the archive you just downloaded and select the 'Extract All' option from the resulting menu. Select the 'c:\windows\system32\drivers' folder and click on the 'Extract' button to extract the Vista 'raspppoe.sys' file.
6. Disable security software, such as a custom antivirus and firewall. Some antivirus and firewall tools might generate conflicts and cause the error 651. If the problem is solved after you disable the tools, update or replace them.