Sounds like the router's dead.
Here's how I get a cable account working with wired connections and a new router. If this doesn't work, you've proved the modem is fine and the computers are fine.
Reset the router to factory defaults by holding the reset button down for 15 seconds with power on.
- Turn off everything, the modem, router, computer.
- Connect the modem to the router's WAN/Internet port.
- Connect the computer to one of the router's LAN/Network ports.
- Turn on the modem, wait for a steady connect light.
- Turn on the router, wait for two minutes.
- Boot the computer.