|From the sounds of it, your router may be broken.|
Click on my name above in this response and read my “how-to” guide titled, “Troubleshooting Wireless Issues” and go through the steps listed there. The troubleshooting steps work for basic router issues.
I suspect the reason only one device is able to get internet connectivity when connected directly to the modem is that your ISP only allows one or two MAC addresses to connect to it. You would have to call them to verify that. If that is the case and you have to replace your router, you'll want to have them reset the MAC mapping on their end or, spoof the external MAC address of your broken router onto the replacement.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.