How to Troubleshoot a dead Internet connection

I hate network problems. They’re the worst. When they happen in my house, I tend to use a vocabulary that would shock Quentin Tarantino.
A wide variety of problems can block Internet (and local network) communications. Your first job is to find the cause. Follow these steps in this order, and you should at least figure out what is the causing the problem.

Reboot the network: Shut down your PC, unplug the router, then unplug the modem. Wait a minute. Then plug in the modem. Wait another minute, and plug in the router. Then boot the PC. Hopefully, that will fix the problem. If not, read on.
Eliminate Wi-Fi: It’s best, during these tests, to make things as simple as possible. A wired Ethernet connection is more reliable than Wi-Fi. So bring your computer into the same room as the router and physically plug it into one of the router's LAN ports.
If you get access, the problem is with your Wi-Fi connection (perhaps you're using an incorrect password, or you're just out of range).
Check other computers: If you have more than one PC at home, can the other one access the Internet? If not, can they at least see each other on the network? (Another test: If you have a network printer, see if you can print to it.)
If you don’t have a second PC, invite a friend with a laptop to your house and see if they can access the Internet. Make sure to use the Ethernet connection.
If the other PC can access the Internet, the problem is with your computer. If two computers can see each other over the network, but neither sees the Internet, the problem is with the router, your ISP, or something in between.
Check the operating system: If you’ve determined that the problem is with the PC, boot with a live Linux distro. If Linux can access the Internet, the problem is with Windows (or whatever OS you’re using). Otherwise, it’s with the hardware.
Eliminate the router: Connect your PC directly to the modem with an Ethernet cable. Then reboot. If you get the Internet, the problem is with either your router or the other Ethernet cable. (I know you have two; you had to set one aside when you eliminated the router.)
Swap Ethernet cables: If you can successfully access the Internet  with one cable but not with the other, you’re in luck. Replacing a bad cable is easy and inexpensive.
On the other hand, if you got a connection with each cable, the problem is with your router.
And if you failed to get a connection with either cable, the problem is with your modem, the cable connecting the modem to your wall, or something completely outside of your control.