Error code 651 is a problem with connection to the net by the modem. This could be a few things which are causing it. First I would reset/cycle your modem and router (if you have one). Keep your computer on and all connections into it. Unplug the modem and router (if you have one) both for at least 10 - 15 seconds. Plug the modem back in first, wait for the lights to do their initial start up test light dance, until the green light is on solid (Not the power light, this is the cable/signal light). If this does not come on than you have a bad modem or a problem with your internet provider's signal. (Call them). Once the cable/signal light is solid, make sure your router, if you have one is connected by Ethernet cables to the modem and plug in your router. Let it do it's light dance and when it is done check to see if your internet is working. If not, if you have a software for your router open it and find and click repair connection. (All modem types are different so not too many details about that. You can find that info by searching for manual for your router type online. It will tell you there.
If the problem is not with the service, modem, router, or router connection reset/repair than next I would open the device manager. Windows 8 just go to the right side of the screen, till the right bar pops up. Enter Device Manager under the search. Device manager is not under apps, so you may have to click settings and you'll see it. In device manager, look for any devices with the little caution symbol under network adapters and other devices. That means the device driver is not working, uninstalled, or disabled. If you see one, try to update driver. If that doesn't work, or it says it is up to date, try to uninstall the driver for that device and then install it again. If it was in network adapters, you may think you lost it, but since you uninstalled it just look at other devices and you'll see it there to click install. Other than that, I would say go to the 'network and sharing center', another setting found through the search on right desktop pop out bar or right click the little wireless bars or LAN Ethernet Plug icon in the bottom right program icons. See what it says for connections. Try set up new internet connection. Just follow the directions. Last thing I can think of, is a problem I ran into when I upgraded from Windows 7 to Windows 8. The drivers, for my devices (Bluetooth and Built-in Wireless Connection) were not working. I freaked out, because the upgrade told me to confirm uninstalling those drivers as they weren't compatible with Windows 8. I was so scared that I LOST my wireless connection on my laptop. Well, I figured out that Windows 8 had the drivers included with the installation, for my devices. I guess because of the new way of Windows, where everything is an app, they determine your computer exactly and have what drivers you need, with the installation.
Anyway, unplug the router, and modem again. While it is all unplugged, restart your computer. Once fully restarted, plug in only the modem, wait for the solid light (like before), plug in the modem, wait for the lights. If no internet still, find and press the hard reset on your router. It is one of those hidden buttons you push in with a pen. Let it reset. That makes it factory setup. It knows nothing. So if you have a router SSID, Protection Security Key, or Password you will have to reset all that. If you do not have the software for the router on your computer you will need it. Open the program. If it is on your computer, it knows the router settings which were just reset, so you need to delete the router profile from it, and start new. Set up an internet connection, whatever type you use.
So that is all I can think of. I am sure that after all that you will be surfing the net!!! :-)