Is this router broken?

My friend gave me a router because I need a new one. Its a linsys WRT55AG. I connect it to my modem. In the back theres 4 ports and an internet port. When I put the ethernet cable for the internet in the internet port, I get a yellow internet icon and am not connected to it. When I put the ethernet cable in any of the 4 ports, the internet works. I only have another cable which connects to my other computer which is also in 1 of the 4 ports. The computers are in the same network and I can access each other, but my other computer doesn't receive internet. If I put the calbe in the internet port, the network doesn't even detect the second computer. Is the router broken? I can't connect to 192.168.1.1 while connect to the internet on my main computer (only if I place the modem wire to the internet port I can then access 192.168.1.1, however, I don't get an internet connection). All the TCP/IP 4 / 6 / DNS are set at obtain IP automatically, no password protections. Anyway to solve this? or new router?