internet connection problems

Yuu guys, I have a little problem and google didnt answered my questions so please help me :>

At home we are using a cabled router. When my computer wants to connect to the internet there is no problem. When I also enable an other computer the internet shuts down. Now I have read somewhere that a thing that can cause this problem could be that both computers are using the same ip and that I should change that. Is that true and how can i do that?

Thnx for helping me!