Don't know if the modem will respond to pings to be honest. If the connection is working properly with one PC then it's just a case of registering the router with the modem.
Try the power cycle routine first,
Shutdown PC,
power off router,
power off cable modem,
wait 2 or 3 mins (5 to be really safe)
power up cable modem,
wait for lights to settle/ lock,
power up router,
wait for lights to settle,
power up PC.
It's the same routine when switching any equipment on the modem connection as the new equipment has to be registered/ provisioned against your account.
http://homepage.ntlworld.com/robin.d...ips/badip.html has more info on swapping equipment on the modem connection.
If all else fails, connect the original PC back to the modem, when it's working do an Ipconfig /all from a CMD box and note down the MAC address. Clone this into the router and then save and restart everything, after that the connection should work properly as the modem will see the router as the PC that it already works with.