Error 651 is quite an annoying error, but you can quite easily fix it on Windows following a few instructions
Solution 1: Remove Any Existing PPPoE connection, Add New One
1. Step Open the Network Sharing Center, Windows 7 users can simply open the Control Panel and then click Network Sharing. On Windows 8, right-click the network indicator and click Network Sharing Center, this also works on 7:
2. Step Click the blue link Set up a new connection or network
3. Step Click Connect to the Internet
4. Step Click Set up a new connection anyway if you already have a connection and did not want to delete your old one
Solution 2: Ten Second Power Off
Quite often, hang-ups can be caused by internal or firmware problems. It is generally a good idea to plug everything out once a week for 10 seconds to avoid problems
Make sure to actually count the seconds. If you just plug out your modem and other DC adapters but don’t wait long enough it won’t have any effect.
Solution 3: Update Realtek Drivers
Realtek drivers are known to cause problems if you use an old driver or your modem does not support a new drivers and requires an older driver. Both cases are possible, so you should try the newest driver first and then lookup the manufacturing date of your network card to see what driver is required
All drivers can be downloaded from http://www.realtek.com.tw/