The main issue here is lack of diagnostics. I'm not a windows user, so my windows diagnostic skills are weak.
When I am resolving network issues I follow up the stack (well, maybe back down it, if
http://www.google.co.uk/ works there is not point going lower.
Physical
Connectivity - it's physically connected (wired only obviously) and you have a "LINK" light both ends of the cable? Does wiggling the connectors cause link light instability?
You can exclude the OS completely by checking the Ethernet LINK light status when at the BIOS post screen.
OS Hardware layer - Does the OS see the the device? In Linux the first place to look would be "dmesg" or "lspci" for the hardware ident and driver selection. In windows I would assume Device Manager or maybe a payware hardware diagnostics/monitoring tool like Everest? If the device is missing here, use another network connection (your phone?) to google the motherboard, network adapter name and "Problem".
Link layer - Does the Ethernet device appear to be function? In Linux "ifconfig" will show Ethernet devices whether connected or not and show most of their internal state. You 'might' be able to get some of this in the network connection properties or details dialog in Windblows. You should see stuff about "Link state" and a hardware address like "fc:aa:14:26:64:1b". You might also get useful things like Tx/Rx packets/frames and importantly Tx/Rx errors. Anything wrong here could be hardware, cables, firmware or driver related. As the first is not going to easy, save buying a new card, you swap cables/switches, update the OS drivers or search for known issues such as mentioned in this thread.
Network Layer -
Assuming "IPv4" does the device have an IP address? In windows you can get this with "ipconfig" at the CMD prompt. In linux "ifconfig" again. Does the address look familiar or "normal", eg: 192.168.x.x, 10.x.x.x, or 172.16-32.x.x, if it's a 169.x.x.x address it's likely a dummy and you have a problem. If it's 0.0.0.0 or blank then you have no network layer setup.
If you don't, you can assign one, but you will need to know the address and mask of the router. However this should be auto assigned. WARNING!*
Do you have a default gateway? This is your router IP for 99% of Domestic/SOHO set ups. It should be assigned automatically, see the warning.
Can you ping your own IP, can you ping the router IP? If yes, you don't have a problem with the IP layer.
Can you ping 8.8.8.8? If yes, you have internet too.
Can you ping google.co.uk? If yes, the internet is fully working, you have an application or firewalling issue.
Transport Layer - TCP/UDP connections. Unlikely to go wrong on it's own in domestic / SOHO setups but could be firewall issues.
Application layer - DNS is the lowest level service without which the internet doesn't work very well. It also should be auto assigned.
If you can ping 8.8.8.8 but not google.co.uk you probably have a DNS issue.
*WARNING: DHCP is the thing that gives devices network settings automatically. Routers typically tell new devices to use it's network, assign it an IP address, tell it the default gateway and the DNS servers. It is also finickity and can ruin your day when it goes wrong. Here's why:
Do you have more than one router in your network? More accurately do you have more than one device which runs a DHCP service? These would include routers, cable modems,
Wifi Access Points and a number of others.
If you have more than one DHCP server, unless they are configured properly, it will be pot luck as to which one answers the new device. If the wrong one answers, chances are it will issue poor or unusable settings, such as "default gateway" and DNS servers.
I have a separate ADSL model and Wifi access point. For the first few months everything worked great, then randomly I stopped getting the correct IP address or default gateway and had to restart the network interface (or reboot). Knowing what I'm doing it didn't take me long to narrow it down to the WiFi access point having a DHCP server.
So how do you fix it? I configured the Wifi access point to forward DHCP requests to the router. The alternative is to turn the DHCP service off, if you can, configure it's server IP address range, gateways and DNS manually or... just assign your own IP addresses on the OS manually. The later removes DHCP completely from being an issue ever again, but is less and less practical with more and more IP devices showing up in your home, Sky boxes, TVs, mobile phones, IoT devices etc. etc.