What you were asking depends on what internet connection you have and provider. A few years back on ADSL NOT 'always on' you needed to have a username and password on your computer but nowadays this is all done in the router or you don't need it, it is always on and settings are kept on your router.
I see you said you can connect to the internet with another PC there so your router seems OK
-Good one in activating windows through the phone, I have done this like 10 years ago with XP because I didn't have internet
You can first of all make sure your network adapter drivers are installed, by going to Device Manager and look for Network Adapters. If there are no drivers for your Network card then you need to install them as this would be why you cannot get connected.
If the Network adapters are fine (no exclamation mark or whatever) on Device Manager, try forcing it to renew its IP address:
Open up Command Prompt, type 'ipconfig /release' wait a while for it to release its IP settings and then do 'ipconfig /renew' to retrieve IP settings for your PC from your DHCP service on your router.
Once that is finished do just ipconfig and check what is the IP assigned. If you get a 169.xxx. ip address then the issue persists
I hope this helps you to get through this.