There are many reasons that may cause the Error 678: a network cable is disconnected, the modem is disabled or its drivers are corrupted, there are spyware on your computer, the connection is blocked by a third-party firewall software and so on. In order to fix the problem, go to Start, type ncpa.cpl, right-click the Local Area Connection and select Enable. After that, make sure that the network cable is connected and reset the modem. Another solution is to uninstall and then reinstall the modem and its drivers using Device Manager. For this purpose, right-click the Computer icon, select Manage and then open Device Manager. Expand the Network Adapters list, right-click on the driver and select Uninstall. After that, reboot your computer, press Scan for hardware changes icon from Device Manger and reinstall the modem drivers. If you no longer have the drivers, you can find and download them using Google.
If the error persists, go to Start, type netsh winsock reset, press Enter and reboot the PC. This command will repair the Winsock and TCP/IP. After that, try to temporarily disable your security program and open Internet Explorer. Click the Internet Options from the Tools menu and press Delete Files from the General tab. For further solutions, check the Microsoft Support page.