Hello antoinejones,
Sounds like your ethernet card is not talking to the router. If you have the router manual it will tell you how to reset the router to factory setting. Do that first. Remember, we are working blind here. We need the router model and cable modem model. I't may be as GaRHaR says. The router and modem may not be compatible. Make sure the cat5 cable is hooked from the PC to a lan port on the router. Open your browser the enter 192.168.0.1 in the address bar. If you are asked for username and password I believe for lynksys routers enter admin for password. Leave the other space blank. This is after factory reset.
Make sure the ethernet card is configured with tcp/ip. Also let me know if there is any continous flashing lights on the router when you turn it on.
Good Luck,