(This is for if you're running Windows)
First of all, when you have the ethernet cable connected, is there a green/yellow/orange light at the ethernet port after you've plugged it in? If you don't see one within about 5-10 seconds, this means one of two things: 1- you don't have a link between the network card and the router/switch (bad cable?) or, 2- your network card is disabled in Windows, or doesn't have the drivers loaded.
Now, if you have a link light on at the port, from there it comes down to IP settings. You'll need to see if you've got DHCP enabled on the Ethernet card (it is on by default, so if you haven't changed this, ignore this part). Go to Start and type 'cmd', then press Ctrl-Shift-Enter. This will bring up the Command Prompt. In the command prompt, run this: ipconfig
It will give you a list of all the IP addresses attached to the network devices on your computer. If the address for the Ethernet Card starts with '169', it means that your computer isn't getting a proper IP address assigned from the router. Try rebooting your router and see if this fixes it.
If the address starts with '192', then it'll likely be a firewall issue. Run these two commands to completely reset your Ethernet Card:
netsh int ip reset
netsh advfirewall reset
Now reboot your computer and it should be working.